Computer aided design of soldier pile and lagging ... · Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 1991 Computer aided design of soldier pile

Calhoun: The NPS Institutional Archive

Theses and Dissertations Thesis Collection

1991

Computer aided design of soldier pile and lagging

retaining walls with tieback anchors.

D'Amanda, Kevin J.

Springfield, Virginia: Available from National Technical Information Service

http://hdl.handle.net/10945/28054

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COMPUTER AIDED DESIGN OF SOLDIER PILE AND LAGGINGRETAINING WALLS WITH TIEBACK ANCHORS

THE5I5

BY

KEVIN J. D' AMANDA

A REPORT TO THE GRADUATE COMMITTEE OFTHE DEPARTMENT OF CIVIL ENGINEERING INPARTIAL FULFILLMENT OF THE REQUIREMENTSFOR THE DEGREE OF MASTER OF ENGINEERING

UNIVERSITY OF FLORIDA

FALL 1991


BY

KEVIN J. D' AMANDA

A REPORT TO THE GRADUATE COMMITTEE OFTHE DEPARTMENT OF CIVIL ENGINEERING INPARTIAL FULFILLMENT OF THE REQUIREMENTSFOR THE DEGREE OF MASTER OF ENGINEERING

UNIVERSITY OF FLORIDA

FALL 1991

T253983

Diml

ACKNOWLEDGEMENTS

I wish to express my gratitude to Dr. Townsend,

Dr. Davidson, Dr. McVay, and Dr. Bloomquist for their

support and for making their classes both challenging

and interesting while still enjoyable. Also to Jim

Hussin and the personnel at Hayward Baker for their

assistance in helping me prepare this program. Lastly

to the rest of the dungeon rats,

Barry "BATman" Mines;Dave "Mr. FDOT" Horhota;Dennis Vander Linde "Forces";Zan "The Zan Man" Bates;Craig "Cheats at Golf" Dunkl enburger

;

Dave "Do I still have a desk?" Weintrub;Guillermo "Just one more year at UF" Ramirez;Pedro "Lost in Peru" Ruesta;Tove Feld "and Streams";and the rest of the crew;

thanks for being an island of lunacy in a sea of

sanity

.

BIOGRAPHICAL SKETCH

Lieutenant Kevin J. D'Amanda, Civil Engineer

Corps, U.S. Navy, was born and raised in Miami,

Florida. He attended Miami Dade Community College and

the University of Miami earning a Associate in Arts

degree with highest honors in May 1982 and a Bachelor's

Degree in Civil Engineering, Magna Cum Laude, in

December 1984 respectively. Upon graduation, he was

commissioned an Ensign, U.S. Naval Reserve and

completed Officer Indoctrination School in Newport,

Rhode Island.

Lieutenant D'Amanda's initial duty assignment was

as an Assistant Resident Officer in Charge of

Construction at Naval Air Station Atlanta from March

1985 to April 1988. In April 1988, he reported to

Naval Mobile Construction Battalion Sixty-Two where he

served as Material Liaison Officer and as Assistant

Operations Officer. After the decommissioning of the

battalion in July 1989, he reported in Navy Support

Facility, Diego Garcia as the Public Works Planning

Officer from October 1989 to November 1990. After

which, he reported to the University of Florida to

pursue a Master's Degree in Geotechnical Engineering.

li

Lieutenant D'Amanda is a registered engineer in

the states of Minnesota and Florida. Upon graduation,

he will report to Commander, Naval Construction

Battalions, U.S. Atlantic Fleet, at Norfolk, Virginia

for duty as Assistant Special Operations Officer.

111

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS i

BIOGRAPHICAL SKETCH ii

LIST OF FIGURES vi

LIST OF TABLES ix

ABSTRACT x

CHAPTER ONE - INTRODUCTION 1

1 .

1

Background 1

1 . 2 Computer Program Requirements 3

1 . 3 Computer Language 4

CHAPTER TWO - BRACED EXCAVATIONS AND TIEBACKS 6

2 . 1 Braced Excavations 62.2 Soldier Pile and Lagging 9

2 . 3 Tiebacks Anchors 11

CHAPTER THREE - DESIGN THEORY 13

3.1 Lateral Earth Pressures in BracedExcavations 13

3.2 Active and Passive Earth Pressures 183.3 Hydrostatic Pressure 183.4 Total versus Effective Stress Analysis.... 193.5 Surcharge Pressure due to a Strip Load.... 213.6 NAVFAC DM-7.2 Recommendation on Flexible

Wall Design 223.7 Other Design Considerations 233.8 Design Methodology for Wall Analysis 243.9 Tieback Anchor Capacity 293.10 Minimum Unbonded and Total Anchor Length. 293 . 11 Lagging Thickness 33

IV

TABLE OF CONTENTS (CONTINUED)

Page

CHAPTER FOUR - COMPUTER PROGRAM 35

4.1 Program Flow and Logic 354.1.1 Main Function 354.1.2 Data Functions 444.1.3 Analysis Functions 45

4.2 Assumptions and Limitations 484.3 Example Problems 51

CHAPTER FIVE - USER * S GUIDE 52

5.1 Program Start-up 525.2 Input Data 53

5.2.1 Wall Data 545.2.2 Soil Data 545.2.3 Wall Analysis Data 555.2.4 Anchor Analysis Data 56

5.3 Output Data 565 . 4 Error Messages 60

CHAPTER SIX - CONCLUSIONS 63

6.1 Review of Objectives 636 . 2 Summary of Design Procedures 636 . 3 Conclusions 65

APPENDICES

APPENDIX A

APPENDIX B

APPENDIX C

APPENDIX D

APPENDIX E

VARIABLE NOMENCLATURE 66

COMPUTER PROGRAM FILE 71

CALCULATIONS AND EQUATIONS 101

EXAMPLE PROBLEMS 117

REFERENCES 154

LIST OF FIGURES

Figure Page

1.1 Tieback Soldier Pile and Lagging Wallfor a Cut-and-Cover Station inPhiladelphia (FHWA/RD-82/047 , 1982) 2

3.1 Nature of Yielding of Retaining Walland Braced Cut (Das, 1990) 13

3.2 General Pressure Distribution onBraced Excavation (Cernica, 1982) 14

3.3 Pressure Distributions on BracedExcavations (NAVFAC DM-7.2) 16

3.4 Draw Down of Ground Water Table inSands due to Natural Seepage orMechanical Dewatering (NYCTA, 1974) 19

3.5 Conversion of a Strip Surcharge Loadto an Uniform Pressure 21

3.6 Effective Width of Soldier Pile thatPassive Pressure Acts Upon (NYCTA, 1974).. 22

3.7 Force Diagram for Stage Two ofConstruction in Sands 25

3.8 Force Diagram with and without aTension Zone for Stage Two ofConstruction in Clays 25

VI

LIST OF FIGURES (CONTINUED)

Figure Page

3.9 Pressure Diagram for Stage Three ofConstruction in Sands 27

3.10 Pressure Diagram for Stage Three ofConstruction in Stiff Clays 27

3.11 Pressure Diagram for Stage Three ofConstruction in Soft to Medium Clays 28

3.12 Force Diagram for Determining theEmbedment Depth in Sands AssumingFixity about the Last Anchor Location 28

3.13 Load Capacity of Anchors in CohesionlessSoil Showing the Effects of RelativeDensity, Gradation, Uniformity, andAnchor Length (FHWA/RD-75/128 , 1976) 30

3.14 Effect of Post-Grouting on AnchorCapacity in Cohesive Soils(FHWA/RD-75/128, 1976) 31

3.15 Determination of the Unbonded and TotalTieback Length (FHWA/RD-82/047 , 1982) 32

4.1 Computer Program's Flow Chart 36-43

5 . 1 Main Menu Screen 52

5.2 Input Variables for Wall Analysis 53

VII

LIST OF FIGURES (CONTINUED)

Figure Page

5.3 Sample Output File 57-58

C.l Average Load Capacity of Anchors inFine to Medium Sands 115

C.2 Average Load Capacity of Anchors inMedium to Coarse Sands 115

C.3 Average Load Capacity of Anchors inSandy Gravel 116

vm

LIST OF TABLES

Table Page

2.1 Steps in Engineering an Excavation(Lambe and Turner, 1970)

3.1 Recommended Thickness of WoodLagging, Construction Grade Lumber(FHWA/RD-75/128, 1976) 34

IX

ABSTRACT

Abstract of a Report to the Graduate Committee of

the Department of Civil Engineering in PartialFulfillment of the Requirements for the Degree of

Master of Engineering.


By

KEVIN J. D* AMANDA

FALL 1991

Chairman: Dr. Frank C. TownsendMajor Department: Civil Engineering

Soldier pile and lagging walls are used to support

open excavations and restrict lateral movements. They

also provide an increased factor of safety to nearby

structures and utilities against excessive deformations

and loss of bearing capacity. The soldier pile and

lagging wall consists of structure H-beams driven into

the ground with wood lagging installed between the

flanges of the beams to retain the soil. With the use

of tieback anchors as bracing, they can provide an

unobstructed area for construction.

The design of the soldier pile and lagging wall

consists of developing a pressure envelope for the soil

conditions and determining the number and location of

the anchors for a given H-beam's section modulus. The

pressure envelopes for braced excavations differ from

Rankine's active state. A braced excavation deforms

more laterally at the bottom of the excavation than the

top due to the installation of the anchors. Peck

(1969) developed pressure envelopes for braced

excavations which can be used for the design of a

retaining wal 1

.

A C++ language computer program was developed to

optimize the design of the soldier pile and lagging

wall. The pressure diagrams for sand and clays

developed by Peck and tieback anchor capacity curves

from the Federal Highway Administration were used in

the program. Also referenced was Naval Facilities

Engineering Command, Design Manual 7.2, for flexible

wall design. By varying the number and location of the

tieback anchors, the wall design may be optimized for

given soil conditions and wall requirements.

XI

CHAPTER ONE

INTRODUCTION

1.1 Background

Soldier pile and lagging retaining walls with

tieback anchors are used to support open construction

excavations and restrict lateral movements of the

surrounding soil. The wall provides a factor of safety

to nearby structures against any loss of bearing

capacity as the result of lateral movements. With the

use of tieback anchors, an unobstructed excavation for

construction can be provided. Figure 1.1 illustrates a

typical soldier pile and lagging wall with tieback

anchors. The basic design of the system is as follows:

a. Determine the given boundary conditions

indicating soil stratification, water level, slope of

the soil behind the wall, and surcharge loads.

b. Compute the lateral earth pressure diagrams

for the braced excavation including any pressure

diagrams from surcharge loads.

c. Design the components, which include the

soldier pile; wale; tiebacks; and lagging, based on the

pressure diagrams.

The pressures diagrams for braced cuts differ

from lateral earth pressures obtained by Coulomb's or

Rankine's theory. Peck (1969) derived lateral earth

pressure diagrams for braced cuts in sands and clays

which can be used to calculate the maximum moment and

reaction forces for the design of the retaining wall

system.

DDD

Temporary

Tiebacks

Existing

Building

Temporary

Hall

Future

S^ S t a 1 1 on

Figure 1.1Tieback Soldier Pile and Lagging Wall fora Cut-and-Cover Station in Philadelphia

(FHWA/RD-82/047, 1982)

The basic concept of bracing an excavation is

based on the excavation causing the removal of a mass

of soil and water from a site. The ground water table

may also be lowered outside and below the excavation to

accomplish the construction. Consequently, these

actions will result in a total stress release and

movements in the surrounding soil. A retaining wall is

typically installed to control these movements.

Satisfactory performance of the wall requires that the

excavation periphery not have any excessive movements

or deformations. Moreover, deformations of the

surrounding soil may be limited so that adjacent

structures and utilities are not adversely affected.

The factors that influence deformations include the

dimensions of the excavation, soil properties, ground

water control, time (time excavation open, time a

section is unbraced, etc.), support system, excavation

and bracing sequence, near-by structures and utilities,

and transient surcharge loads. (Lambe and Turner,

1970)

1.2 Computer Program Requirements

The design of soldier pile and lagging retaining

walls requires the determination of the number and

location of tieback anchors for a given section modulus

of a soldier pile to ensure the pile is not

overstressed. This computer program was developed to

calculate the maximum moment of a soldier pile, depth

of embedment, and reaction forces based on the soil

conditions, depth of the excavation, and location of

the tieback anchors. By varying the location and

number of the anchors, the design of the soldier pile

wall may be optimized.

The computer program will also calculate the

required anchor capacities, bonded and unbonded

length of the tieback anchors, and the section

modulus of the wale system based on anchor spacing

and soil type. Tieback capacity and length is based

on pressure injected tiebacks in cohesionless soils

and post-grouted tieback anchors in cohesive soils.

1.3 Computer Language

The computer program was written and compiled in

Borland Turbo C++. c was originally developed in the

1970's for use with the UNIX operating system. The

definition of C was first presented in The C

Programming Language , First Edition by Brain W.

Kernighan and Dennis M. Ritchie in 1978. The

American National Standards Institute (ANSI)

developed a new standard for the language five years

later which resolved ambiguities in it (Turbo C++

Users Guide, 1991). Turbo C++ implements the latest

ANSI standard for C. It is manufactured and a

registered trademark of Borland International, Inc.

CHAPTER TWO

BRACED EXCAVATIONS AND TIEBACKS

2.1 Braced Excavations

Braced excavation retaining walls are used to

support the sides of temporary excavations in various

construction applications. The vertical face of the

cut is held open by the retaining structure until a

permanent structure can be installed. The permanent

structure may include the basement of a building, walls

of a parking garage, or underground facilities. The

braced structure restricts the inward movement of the

surrounding soil preventing settlement, collapse of the

excavation, and possible bearing capacity failure of

nearby structures. Table 2.1 lists the factors to be

considered in designing a braced excavation. The most

common methods of supporting a temporary excavation are

sheetpile walls, dri 1 led-in-place concrete piles,

slurry walls, and soldier pile and lagging.

Sheetpiles are driven into the ground prior to

excavation, interlocked forming a wall, and then the

soil excavated. They may be supported by struts or

anchors as required. Dri 1 1 ed-in-place piles may be

used with a spacing so that lagging is not required.

Table 2.1Steps in Engineering an Excavation

(Lambe and Turner, 1970)

Step Activity ConsiderationNo.

1 Explore and testsubsoil

.

2 Select dimensions of Structure size andexcavation

.

grade requirements,depth to good soil,depth to meet stab-ility requirements.

3 Survey adjacent Size, type, age,structures and location, anduti 1 i ties

.

condition.

4 Establish permiss-ible movements.

5 Select bracing and Local experience,construction cost, time avail-sequence

.

able, type of wall,depth of wall, typeand spacing ofbracing, and de-watering sequence.

6 Predict movementscaused by excavationand dewatering.

7 Compare predictedwith permissiblemovements

.

8 Alter bracing andconstruction scheme,if needed.

9 Monitor constructionand alter bracingand construction asrequired.

Arching of the soil from the lateral pressures

developed by the pile will retain the soil across the

open spacing (Bowles, 1988). A slurry wall is

constructed when concrete is cast-in-placed in a cavity

retained open by a slurry liquid. After the concrete

cures, the soil next to the wall is excavated. Soldier

pile and lagging uses steel H-piles driven into the

ground prior to the actual excavation. Lagging is

placed between the piles as the ground is excavated.

The lagging may be either wood or steel members.

Anchors or struts are used to support the wall as the

excavation proceeds.

If present, ground water acts against the wall and

thus contributes to the stresses which must be carried

by the wall. It also influences the effective stress

of the soil. The total force felt by the wall is a

combination of the hydrostatic force and the effective

soil stress. If flowing water occurs, a seepage

analysis should be made. Factors which must be

considered in a seepage analysis includes the

permeability of the insitu soil, leakage through the

wall, flow parallel to the wall, excess pore pressures

generated by changes in total stresses, seepage forces,

and the time the excavation will be open and hence the

degree of saturation. The actual pore water pressures

generated will typically be less than static pressures.

(Lambe and Turner, 1970)

2.2 Soldier Pile and Lagging

The procedure for constructing a soldier pile wall

is to drive the H-piles into the ground prior to any

excavating. The piles are driven with the flanges

parallel to the proposed cut. They are usually spaced

between four and ten feet apart. When they have been

driven down to the desired depth (typically five to ten

feet beneath the proposed excavation bottom when in

soil), the excavation begins in stages. The first

stage of the excavation is made to the location of the

uppermost strut or anchor. Timber lagging, cut to fit

between the webs of adjacent soldier piles, is placed

in back of the front flanges of the piles. They are

set one piece of lagging on top of the other with only

a small spacer between them. Straw or a geotextile may

be placed between and behind the lagging to reduce

seepage through the wall. Once the lagging is set

down to the first strut level, a horizontal wale is

installed against the piles and the struts or anchors

placed at the desired spacing. The excavation then

proceeds to the next strut level, with the process

continuing until the final excavation is reached.

(Keorner, 1984)

Primary components of a soldier pile and lagging

wall are as follows:

1. Soldier piles which may be either steel H-

beams , steel tubular pipes, concrete piles, or cast-in-

place concrete piles.

2. Support system of braced struts or anchors.

Anchors may be cast-in-place deadman, piles used as

anchors, sheetpile wall sections, or tieback anchors.

3. Wales which distribute the anchor force as

a line load between the soldier piles. They are

usually structural steel sections.

4. Wood or metal lagging which supports the soil

between the piles. (Boghrat, 1989)

Advantages of using soldier pile and lagging walls

include fewer piles, the lagging does not have to be

extended below the excavation bottom, and the soldier

piles can be driven easier in hard ground than can

sheetpile sections. By varying the spacing of the

soldier piles, underground utilities may be avoided.

Also the use of heavy sections for piles will allow

wider spacings of wales and bracing. (Merritt, 1976)

10

2.3 Tieback Anchors

Temporary tieback anchors are used to support the

sides of deep excavation retaining structures. Tieback

systems deform less than strut braced excavations

because; (a) a force at or above the active earth

pressure is locked off in every tieback, (b) tieback

construction does not require over excavation, (c)

tiebacks are not subject to significant temperature-

caused deformations or loads, and (d) rebracing is not

required for tieback walls. When the depth of the

excavation exceeds fifteen to twenty feet and the width

exceeds sixty feet or when obstructions significantly

impact construction, tieback walls are usually less

expensive than strut braced support systems. Tieback

walls provide a clean open excavation for construction.

Internally braced walls interfere with excavations,

concrete work, structural steel placement, and

backfilling. (FHWA/RD-82/047 , 1982)

Some disadvantages of a tieback anchor system may

include obtaining permission for the placement of the

anchors in the property of a municipality or a private

owner. The location of the anchors may be outside the

boundaries of the project where soil properties were

not obtained. Achieving a satisfactory anchorage

11

capacity in soft clays or submerged sands may also be

difficult to achieve. (Clough, 1972)

The capacity of tieback anchors is dependent on

the size and shape of the anchor, tendon type and size,

insitu soil properties, and installation and grouting

method of the anchor. Design of a tieback system

should include the following:

a. a tieback feasibility evaluation,

b. an evaluation of the risk and consequences

of failure,

c. the selection of a tieback type,

d. the estimation of the tieback capacity,

e. determination of the unbonded and total

tieback length,

f. selection of a corrosion protection system,

g. selection of a tieback testing procedure,

and

h. establishment of an observation and monitoring

system. (FHWA/RD-82/047 , 1982)

Federal Highway Administration report number

FHWA/RD-82/047, Tiebacks, provides detailed guidance

and design procedures for tiebacks.

12

CHAPTER THREE

DESIGN THEORY

3.1 Lateral Earth Pressures in Braced Excavations

When sufficient yielding of a retaining wall

occurs, the lateral earth pressure can be approximated

by Coulomb's or Rankine's theory. However, braced

excavations yield differently than conventional

retaining walls. Figure 3.1 depicts the different

deflections of the two wall types. The deformation of

a braced wall gradually increases with the depth of

excavation. The variation of the amount of deformation

will depend on the type of the soil, depth of the

excavation, and construction of the wall.

Retaining Uall

Uall

Deflection

NJ

vxw

Bracing Cut

VXW

Uall

Deflection

BottoB o( Cut~W>«

TQPPf J^l

Figure 3.1Nature of Yielding of Retaining Wall and

Braced Cut (Das, 1990)

13

At the top of the excavation, deformations are

small thus the lateral earth pressure approaches the at

rest condition. At the bottom of the excavation, the

deformations are greater, but the lateral earth

pressure will be lower than Rankine's active earth

pressure. Therefore the distribution of lateral earth

pressure deviates from the usual linear distribution

(Das, 1990). This is illustrated in Figure 3.2. The

total force exerted against the wall may be 10-15%

greater than active condition. The state of stress

behind a braced excavation has been described as an

arching active condition (Lambe and Whitman, 1969 and

Cernica, 1982).

Rankine J

s

~V7T>tf

Figure 3.2General Pressure Distribution on Braced

Excavation (Cernica, 1982)

14

The pressure envelopes proposed by Terzaghi and

Peck (1967) and as recommended by NAVFAC DM-7.2 (1982)

are assumed for the design conditions within the

program. The earth pressure envelopes for braced walls

in sands, soft clays, and stiff clays are illustrated

in Figure 3.3. For stiff clays, NAVFAC DM-7.2 (1982)

recommends horizontal stresses between 0.2 and . 4"ftH

.

The value of . 4"tf

H is used within the program. The

stability number is calculated as N$

= "tfH/c. Where ^

is the unit weight of the soil, H is the depth of the

excavation, and c is the undrained shear strength of

the soil. Characteristics of these pressure envelopes

include:

a. They apply to excavations deeper than twenty

feet

.

b. The pressure envelopes assume the water table

is below the bottom of the cut. Sands are assumed to

be drained with the lowering of the ground water table

behind the wall. Clays are assumed undrained and under

short-term conditions.

c. Lateral stresses are apparent stresses which

are to be used for the calculations of the reaction

loads

.

15

d. The behavior of an excavation in clays depends

on its stability number. (Lambe and Turner, 1970)

SAND SOFT - riEDIUll

CLAY

0.25H

0.75H

0.65Ka * ut x H Ka* ul * H

Ka = 1 - <4c/ut*H>

STIFF CLAY

0.4 » ut *H

Figure 3.3Pressure Distributions on Braced Excavations

(NAVFAC DM- 7. 2)

The apparent stresses are for entire sand or clay

layering only. Engineering judgment should be used for

tills, silts, or fills; varying soil type with depth;

and when hydrostatic stresses act on the wall.

Lambe and Turner (1970) concluded that predicting

the behavior of braced excavations cannot be made with

16

complete confidence. This is the result of difficulty

in selecting the proper soil parameters, field boundary

conditions, and the details of construction. However,

Ulrich (1989) concluded that the recorded pressures for

overconsolidated clays agree with those developed by

Peck (1969). Ulrich also noted that soil

stratification does not have a significant influence on

the apparent earth pressure in overconsolidated clays.

In another case study in Washington D.C. where the soil

stratification was layers of sands, silty sands, and

stiff silty clays, the measured earth pressures fell

within the apparent earth pressure envelope of 0.2^5*1

for clays (Chapman et al . , 1972). Results from other

excavations in the Washington area revealed that the

apparent earth pressure coefficient varied with the

depth of the cut. A value of 0.15#H for a thirty foot

cut, 0.2tfH for a forty to fifty foot cut, and 0.23"uH

for a sixty foot cut (Chapman et al . , 1972). The

design of braced cuts is predominately based on

pressure diagrams derived empirically as a result of

field tests. Sound engineering judgement should be

used in determining the applicability of a given

pressure diagram for a particular cut.

17

3.2 Active and Passive Earth Pressures

For the initial two stages of construction, the

soldier pile wall will develop earth pressures

approaching the active and passive states. In granular

soil, the soil is assumed to be drained and active

earth pressures are developed as the wall deforms

laterally. This is resisted by the passive resistance

which is developed as the H-beam compresses the soil

acting on an effective area of three times the width of

the H-beam below the bottom of the excavation. However

there exists some uncertainty of how the pressures act

at and below the excavation line (Bowles, 1988). The

active and passive earth pressure coefficients are

calculated assuming Rankine's theory.

In the case of cohesive soils, undrained

conditions (i = 0) are assumed with no frictional

resistance developed. The stresses in the tension zone

are neglected in the design computations with the depth

of the tension zone taken as zt

= (2*c-q)/ }f .

3.3 Hydrostatic Pressure

Hydrostatic pressure is calculated as the unit

weight of water (62.4 pcf) multiplied by the height

of the water table. It is assumed in the program

18

that sand and gravels are drained and the water table

will be drawn down to the bottom of the excavation by

natural seepage or mechanical dewatering. This is

illustrated in Figure 3.4. Clay layering is assumed to

be undrained and analyzed using either a total or

effective stress analysis approach.

Ground Surface

v Bot ton of CutT V/Ofrf

SflND - DRAINED vx*/1

Original Ground Uater Surface _ J_

Uater table draun doun to

bottom of cut due to seepage

through tinber sheeting or

mechanical deuatering.

Figure 3.4Draw Down of Ground Water Table in Sands

due to Natural Seepage or MechanicalDewatering (NYCTA, 1974)

3.4 Total versus Effective Stress Analysis

Some question on how to analyze the wall is raised

when the ground water table is located above the bottom

of the excavation in clay layering. The apparent

lateral earth pressure envelopes proposed by Peck are

19

based on empirical data from total stress analyses.

The use of a buoyant unit weight rather than the total

unit weight of the soil and superimposing hydrostatic

pressure onto the earth pressure diagrams change the

analysis to an effective stress analysis approach.

However the total stress soil parameter of undrained

shear strength is still used. Therefore this effective

stress analysis approach is not entirely correct.

Either a total or effective stress analysis

approach may be used to design the wall. In the case

of a total stress analysis, the saturated unit weight

above and below the water table should be entered. For

an effective stress analysis approach, the saturated

unit weight above the water table and the buoyant unit

weight below the water table should be used. The

location of the ground water table for the effective

stress analysis must therefore be located above the

bottom of the cut.

Generally, the results from using the total unit

weights (total stress approach) are more critical

loading conditions than the approach adapted by using

buoyant unit weights (Liao and Neff, 1990).

20

3.5 Surcharge Pressure due to a Strip Load

To account for the lateral pressures due to a

strip surcharge load located at some distance from the

wall face, an equivalent uniformly distributed pressure

acting on the wall is developed. The total force

exerted by the strip load on the wall is calculated and

then converted to a uniform pressure by dividing the

total force by the height of the wall. The force is

calculated by the equations derived by Jarquio (1981)

and as illustrated in Figure 3.5.

T oFROM:b a

-iWiii

subgrode

82/h

/ J '

S-X.'x

q=PA

P = 2 q * h / pi * (82 - 81 >

82 = arctan [ < a + b ) / h ]

81 = arctan [ b / h ]

Figure 3.5Conversion of Strip Surcharge Load to an Uniform Pressure

21

3.6 NAVFAC DM-7.2 Recommendations on Flexible Wall

Design

The following recommendations from Naval

Facilities Engineering Command, Design Manual 7.2

(1982) were considered in the programming.

a. The total resistance force acts on an

effective area of three times the flange width of the

pile (3*bf) as shown in Figure 3.6. This is to account

for the differences between the failure in soil of an

individual pile element and that of a continuous wall

for which pressure distributions were derived.

3 bf

Figure 3.6Effective Width of Soldier Pile that Passive

Pressure Acts Upon (NYCTA, 1974)

b. For temporary construction, a factor of safety

of 1.5 should be applied to passive pressures. This

option is available within the program but it is not

recommended. Passive resistance is calculated using

Rankine's theory which is already conservative compared

22

to a logarithmic spiral failure surface approach to

estimate passive resistance.

c. Neglect the soil resistance to a depth of 1.5

times the pile width from the bottom of the excavation

for clays and the depth of the pile width for sands.

This, however, is not accomplished in the program. It

was considered that significant conservativeness

already exists within the wall design.

d. The required depth of embedment is calculated

based on controlling the moment within the section to

ensure the pile is not overstressed at the final

anchor location. The active soil pressure will be

resisted by the passive pressure and the allowable

moment of the section.

3.7 Other Design Considerations

Other design considerations included within the

program are:

a. To calculate the anchor reactions, it is

assumed the piles are hinged at the bottom of the

excavation and at all the anchor locations except the

upper anchor. The soldier pile between each pair of

hinges is assumed to be a simply supported beam

(Bowles, 1988 and Das, 1990).

23

b. An allowable stress for the steel soldier

piles of 28,800 psi is used to calculate the required

section modulus.

c. Wales are designed assuming they act as simply

supported beams, pin-ended with maximum moments equal

to w*l /8. This moment is then increased by 33% to

allow for overstressing during preload testing of the

anchors. An allowable stress for the steel of 28,800

psi is used to calculate the section modulus from the

maximum moment

.

3.8 Design Methodology for Wall Analysis

For the first two stages of construction, the

active and surcharge forces are being resisted by the

passive and reaction (stage two) forces. The reaction

force is calculated by summing moments about the point

of net zero forces on the embedded pile assuming it is

hinged there and thus zero bending moment. The maximum

moment within the pile can be calculated by summing the

moments about the point of zero shear. From the

maximum moment, the required section modulus is

calculated. The embedment depths are calculated for

stage one by determining the point where the net moment

is zero and for stage two by assuming fixity at the

24

anchor location and summing moments there so the pile

is not overstressed. For clays, the stresses within

the tension zone are neglected in the calculations.

The force diagrams are illustrated in Figures 3.7 and

3.8 for sands and clays respectively.

7X^71

Ph=KalsXq«H

P<, = Kd l s « ul * H-2yJ

Ka«t>(«(q+ut*H>*0

Ka*bf*ut«D^2/2

net pp - (3Kp/<s - Ka> * b< ut 0*2 /7

Figure 3.7Force Diagram for Stage Two of Construction in Sands

Ui th Tension Zone: Uithout Tension Zone:

(q-2c>«s

(ut»H + q - 2c)«s

Zt = C 2c - q ) / ut

Pp = < 6c/fs +2c-q-utiH>«bf«D

Figure 3.8Force Diagram with and without a Tension

Zone for Stage Two of Construction in Clays

25

Kiewit design procedures are also used to

calculate the maximum moments and reaction force for

the initial two stages of an excavation. Kiewit

procedures were developed by Peter Kiewit Sons'

Company based on empirical data and field results.

In the first stage, it is assumed that a pinned

connection exists in the pile two feet below the

bottom of the excavation. The maximum moment is

calculated at this point. In the second stage, the

maximum moment is taken as M = w*l /9. Where w is the

average pressure on the span from the first anchor to

the bottom of the cut and 1 is the distance between the

anchor and the bottom of the cut. The reaction force

is calculated assuming pinned connections at the anchor

location and the bottom of the cut.

After the second anchor is in place, the pressure

distribution will correspond to those for braced cuts.

Reaction forces are calculated by assuming pinned

connections and summing moments about the anchor

locations. Next the point of zero shear is found and

moments summed about it to calculate the maximum

moment. The pressure diagram for sands is depicted in

Figure 3.9 and in Figures 3.10 and 3.11 for clays.

Embedment depth is determined by summing moments at the

26

last anchor point assuming fixity so the pile is not

overstressed . This is illustrated in Figure 3.12 for

sands

.

sigs sigh

Rl

R2

vx^rf

VX.W- sigs = Ka*q«s

sigh - 0.65Ka*s«ut«h

sig = Ka»s«(q * 0.65ut»h)

pp = 3Kp/fs « <ut«bf*D*2/2)

Figure 3 .

9

Pressure Diagram for Stage Three of Constructionin Sands

Ns <= 6

Rl

VXX/1

\ pa = 0.1 * s i ut H

"1

0.25H

0.5H

0.25H

v^wpq = s * q

u = s « utu « hu

pp net = <6c/fs + 2c - q) • bf

Figure 3.10Pressure Diagrams for Stage Three of Construction

in Stiff Clays

27

Ns > 6

Rl

R2

^7XW

pa = Ka * ut * H

Ka = 1 - 1c / <ut * H)

0.25H

0.75H

VXV/1

pp net = <6c/fs * 2c - q) * bf

Figure 3.11Pressure Diagram for Stage Three of Construction

in Soft to Medium Clays

Mmax

ANCCj] Prtl = Ka « s « <0.65ut«h + q> rf

Pp = 3Kp/fs*<ut*bf*[h2/2)

Calculate D —+~ n*ax f Pp*<2/3D Hf)- PAUtf /2 =

Figure 3.12Force Diagram for Determining the Embedment Depth in

in Sand Assuming Fixity about the Last Anchor Location

28

3.9 Tieback Anchor Capacity

In cohesionless soils, the tieback anchor

capacity is calculated assuming pressure injected

tiebacks using an effective grout pressure in excess

of 150 psi . Figure 3.13 shows curves developed by

Ostermeyer (1975) as an function of length and soil

type. An average of these values was used to develop

equations for each soil type to calculate anchor

capacity in the program. These values assumed anchor

diameters between four to six inches and a depth of

overburden greater than thirteen feet.

In cohesive soils, tieback capacity is based on

post-grouted anchors with grout pressures in excess of

150 psi. Figure 3.14 illustrates tieback capacity

based on clay consistency. An anchor diameter of six

inches was assumed to calculated tieback capacity.

3.10 Minimum Unbonded and Total Anchor Length

The unbonded length of the anchor is calculated

based on locating the bonded length of the anchor

outside the failure zone behind the back of the wall.

The location of the failure zone is based on using

the failure surfaces from Rankine's theory. Report

number FHWA/RD-82/047 recommends that the length of

29

400

« 300Q

200

^ 100-

D

-

-

-

^nff^

Wm

10 15 20

Length cW Anchor GO25

Uery Dense

Uery Dense

fled. Dense

Dense

fled. Dense

fled. Dense

30

Dianeter of Anchor: 1 - 6 in.

Depth of Overburden: >= 13 ft,

Sandy Gravel

Cu = 5 - 33

flediure to

Coarse Sand

Cu = 3.4-4.5

Fine to

Mediui SandCu = 1.6-3.1

Figure 3.13Load Capacity of Anchors in Cohesionless Soil

Showing the Effects of Relative Density,Gradation, Uniformity, and Anchor Length

(FHWA/RD-75/128, 1976)

30

Stiff U. Stiff

to Hard

Clay Consistency

Figure 3.14Effect of Post-Grouting on Anchor Capacity

Cohesive Soils (FHWA/RD-75/128 , 1976)in

31

the anchor be of sufficient length to locate the anchor

in soil which would not be affected by movement of the

wall. The unbonded length should place the anchor

beyond the critical failure surface as illustrated in

Figure 3.15. Also recommended is a minimum unbonded

length of fifteen feet to avoid load losses as a result

of long term steel relaxation, creep in the soil,

anchorage seating losses, and structural deformation.

Critical Failure Surface

Uall Face

VXWMost Probable Failure SurfaceThrough the Ends of the Tiebacks

Figure 3.15Determination of the Unbonded and Total Tieback

Length (FHWA/RD-82/047 , 1982)

The total anchor length should be of sufficient

length to ensure a satisfactory factor of safety

against sliding along the most critical failure

surface through the ends of the anchors. If the factor

32

of safety is insufficient, the total anchor length

should be increased (FHWA/RD-82/047 , 1982). This is

also illustrated in Figure 3.15.

This computer program does not calculate the

factors of safety against failure of the tendons,

failure in the anchor zone, or overall external

stability against wall failure. Boghrat (1989)

recommends the use of the STABL computer program to

calculate of the total anchor length to achieve a

minimum factor of safety. The user manual for PCSTABL4

is presented in the Federal Highway Administration

Report No. FHWA-TS-85-229 (Carpenter and Kopperman,

1985)

.

3.11 Lagging Thickness

The required thickness of the wood lagging can

be estimated from Table 3.1 from report number

FHWA/RD-75/128 (1976). The table is based on soil

type, depth of the cut, and soldier pile spacing.

33

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34

CHAPTER FOUR

COMPUTER PROGRAM

4.1 Program Flow and Logic

The computer program logic and flow is illustrated

in the flow charts shown in Figure 4.1. Appendix A

contains the variable nomenclature for the program and

the actual program file is included in Appendix B.

Appendix C contains various calculations and equations

used within the analysis functions in the program.

4.1.1 Main Function

The program starts with the main function which

includes the main menu and exit routines. The main

menu routine displays the main menu screen which

prompts the user to input the next step. The options

include enter soil and wall data, read data from an

existing file, edit the input data, save the data in a

file, execute the wall analysis, execute the anchor and

wale analysis, save the analysis results, or exit

the program. The program will execute the appropriate

function upon input. The program will request

verification before exiting.

35

MAIN MENU

1. Enter Soil Properties 8 Wall Data

2. Read Data From an Existinq File

3. Edit Inputted Data

4. Save Inputted Data

5. Execute Uall Analysis

6. Execute Anchor / Wale Analysis

7. Save Analysis Data in Output File

8. Exit Program

\

Input Next Step

0* *®

©

Figure 4.1Computer Program's Flow Chart

36

Cl> INPUT FUNCTION

INPUT DATA:

HALL:

EngineerProjectDateTop ElevationBottom ElevationNunber of AnchorsAnchor ElevationsSpacing

SOIL:

Elevation of GUT

Number of Soil LayersSoil Tgpe

Soil Properties(elev., unit ut.,

friction angle or cohesion)Backs lopeSurcharge

MAIN MENU

READ_DATA FUNCTION

REENTER FILENAME

Read Data File

I(lain Menu *

ABORT

Figure 4.1 (Continued)Computer Program's Flow Chart

37

d> UIEU DATA FUNCTION

/Input It

*7 Neu Ua

em No. a

value /

/'input II

V Neu Ua

en No. 8

alue

G> SAUE DATA FUNCTION

»^/ Input Filename/


38

©- ANALYSIS FUNCTION

r~~

'INPUT;

Estiriated uidth o( pile

Factor of safety against passive pressure

Depth of overexcavai ion belou anchor location

CLAY ANALVSISCLAY

SAND ANALYSIS

Display Results From Anchor Analysis

IOUTPUT: ;?ero riax. Section Enbednent

\ Shear Moment Modulus Depth

Iha in menu

ReactionForce

©- ANCHOR FUNCTION

Calculate Uale Section Modulus

S = P. I 1 Itj ) d » 2 / H.I s

ICalculate Anchor Capacity

Pu = PJiHj] * d / s cos

I

inq of Anchorslnation of Anchors

Type:

Fine to Mediua Sand

ftediun to Coarse Sand

Sandy 6ravel

Medium Clay

Medio* to Stiff Clay

Staff Clay

Stiff to Uery Stiff Clay

Uery Stiff Clay

Uery Stiff to Hard Clay

Calculate Anchor Length Calculate Unbonded Length^^1

IOutput fron Analysis:

Anchor Section Anchor Anchor Unbonded

Rou Modulus Capacity Length Length

IMAIN MENU


39

Ci> SAUE fUNCTlON

Irlnput Filename/


40

ANALYSE *>H SAND-ANALYSE

'.tog* l

STOP

FUNCTCN

Determine rjepHi of First Cut

KA_KP rUMCTION

Cdaioto SoH ft Surcharge rorces

ond rat passive pressure

IDetermine location of z«ro shear ( z )

CotaloJe Mmox at point of zero shear

Cotaiore Sreq from Umax

Determine for Z«ro Moment at D

Determine Mmax using Klewt Crfterfa

-e»»]stooe I I

f

-

i[Determine Depth of Cut

[ KA-W RJMC1I0N\-i

STOPFUNCTION

Calculate Soil ft Surcharge Forces

and Net Passive Pressure

IOetermine Ft. ( X ) where Net Forces =

Calculate Reaction by Summing Moment ot X

Find PI. of Zero Shear

CctoukJte Mmox at Zero Sheer

Calculate Sreq from kftnax

Oetermine D by Summing Momenta about AHC(0]

Detarmfne Mmox and R1 using Kievil CrNeria

Stage III*

1 = 2

Calculate Depth of Cut

f~KAJCP FUNCnrjN

STOPrUHCTION

1 = 1+1—I

—

Urtcutat* Soil ft Surcharge Foroee

ond Net Passive Pressure

1CJcubte Reaction Farces by Summing Moments

abaul Anchor l ocottens Assuming Pinned Connects.

find PcW of Zero Shear.

Cofcubte Mmax al Pi of Zero Shear.

Cabubte Sreq Irom Mmax.

JZ£

YES

MN_D FUNCTION ^ Cdcutate Df i J ft Dmh

Rrtur r. to ANALYSIS FUNCTION


41

ERROR - So4l wH not

Support Wol

Determine location of zero shear ( z )

Calculate Mmax at point of zero shear

Calculate Sreq from Mmax

Determine D for Zero Moment at D

Calculate Mmax using Kiewit Criteria

Stage I

}Determine Depth of Cut

WT_C_C8 FUNCTION^ STRP

RHCTTON

ERROR - Soil wil not

Support Wall

Determine Pt. ( X ) where Net Forces =

Calculate Reaction by Summing Moment at X

Find Pt. of Zero Shear

Calculate Mmax at Zero Sheer

Calculate Sreq from Mmax

Determine D by Summing Moments obout ANCfO]Calculate Mmax and R1 using Klewtt Criteria

Slogs UN

CdaJate StoMftjr Numt*r, *

ICafculate Sod Pressures:

H Ms <= 6, Stress = 0.4 wt Htf Hi > 6, Stress = Ka » wt » H

ICatciJott Reaction Force by 5nnrih9 Moments

about Anchor Locations Assuming Pinned ComocHons.

FM PuM of Tmo Sraor.

Cofcutot* Mmax at PL of Zero Shear.

Cofcutott Sreq from Mmax.

Detimifria D(| ] by Sunnmlng Moments about ANC( |-1

J.

Wirn to ANALYSE FUNCTCN Mirm1r» OmJn from Mmax far Al Stoats of Fxoovorkn


42

SAJO-AMM.YSG KA_KP FUNCTION

II

Cdcutate Avorogi Unit Wt

aid Friction Angto

I \ Above / ^^ A«roq» Wt. ft F.A.

CofcutntB Ko

IFind Bottom Wt * FA

ICdoulataKob* Kpb

1R«*xn to SArC_ANAI.YS6

CI.AY_AMAl.YSIS WT_C_Cfi FUNCTtCM

IColcufcit. Avcrogs Unit Wt

and Con—ton Vdu*

Wt. A Ca Ar«rooe Wt. & Co

Return lo a AY AMA1 YSC


43

4.1.2 Data Functions

The data functions will input, read, edit, and

save the input data or save the analysis results. The

input function prompts the user for the input of the

various wall and soil data. The read function prompts

the user for the filename of the data. If the file

does not exist in the working directory, an error

message is displayed and it requests the filename be

reentered or the function aborted. Upon finding the

file, the data is read and entered into the appropriate

program variables. The view data function displays the

wall and soil data and requests if any changes are

desired. If a change is desired, the number of the

item and then its new value are entered. The save data

function will save the input data in a DOS file in the

working directory. If the file already exists,

verification will be requested before coping over it.

Lastly, the save function will save the results of the

analysis in a DOS file. The save routine will request

the filename and verification before coping over an

existing file. After executing a particular routine,

the program returns to the main menu.

44

4.1.3 Analysis Functions

The next series of functions perform the various

analysis calculations. The analysis function requests

entry of the estimated thickness of the pile, the

factor of safety against passive pressure, and the

depth of over-excavation below an anchor depth.

Following input, the function determines the soil type

and executes either the sand analysis or clay analysis

function. After executing the sub-function and

completing the calculations, flow is returned to the

analysis function and the results are displayed.

The sand analysis function executes its analysis

in three stages. The first stage is for the initial

stage of excavation before the first anchor has been

installed. It calculates the point of zero shear,

maximum moment at the point of zero shear, required

section modulus from the maximum moment, and the depth

of embedment at the point of zero bending moment. Stage

two is for the second stage of excavation after the

first anchor is installed. It calculates the same

items as stage one plus the reaction force. The

embedment depth is based on not overstressing the

pile at the anchor location assuming fixity there.

Additionally for the first two stages, the moments

45

and reaction force are calculated using the Kiewit

criteria. Stage three is executed for the stages of

construction after the second and thereafter anchors

are installed. The pressure distributions for braced

cuts are used in this stage. The reaction forces,

point of zero shear, maximum moment, and required

section modulus are calculated in the function. The

embedment depth is calculated by calling the sub-

function, "min_D". It calculates the embedment depth

from the maximum moment for each particular stage.

After the final stage is completed, the minimum

embedment depth is calculated from the maximum moment

for all the stages of construction. The sand analysis

function uses the function "ka_kp" to calculate the

average unit weight, friction angles, and coefficients

of passive and active earth pressures. The base

friction angle and unit weight are the properties of

the soil layer at the bottom of the excavation.

If the soil type is clay, the function clay

analysis is executed. It performs essentially the

same calculations as the sand analysis function. It

first determines the location of a tension zone, if

it exists, and excludes the stresses within it from

any calculations. Also it verifies the soil will

46

support the excavation based on the net passive

resistance of the structure being greater than zero

(p . = 6c/fs + 2c - q > 0). An error message is

displayed if it will not. In the third stage routine,

the stability number of the cut is calculated and the

pressure diagram corresponding to the stability number

determined. The function "ca_cb_wt" is used to

calculate the average unit weight and shear strength of

the cut and the base shear strength. The base shear

strength is calculated from an average over a depth

twenty feet below the bottom of the excavation.

Both the sand and clay analysis functions use the

function "strip" to convert a strip surcharge load to

an equivalent uniform surcharge load. This surcharge

load is then included in the design calculations.

The anchor analysis function is used to calculates

the section modulus of the wale for each row of

anchors, the required anchor capacity, the bonded

anchor length based on soil type and anchor capacity,

and the unbonded anchor length. Prior to the actual

analysis, anchor spacing; the inclination angle of the

anchors; and soil type are entered. After completion

of the various calculations, the results are displayed

before the program returns to the main menu.

47

4.2 Assumptions and Limitations

1. The coefficient of passive earth pressure is

calculated assuming Rankine's theory which is

conservative compared to a logarithmic spiral failure

surface approach in estimating the passive resistance.

2. An average unit weight and friction angle (or

cohesion) for the cut is used in the soil pressure

calculations. The base values for sands are the

properties of the sand layer at the bottom of the

excavation. For clay layering, the base value for

cohesion is calculated by averaging the cohesion values

over a twenty foot depth below the bottom of the

excavation. This is to account for soft or stiff

layers just below the bottom of the excavation. The

difference between a soft and very stiff clay layer is

more significant than that between a loose and dense

sand. It is recommended only minimal soil layering be

used

.

3. A cut of entirely sand or clay layering is

assumed in the program. The computer program will

not accept mixed soil layering or silts. As an

alternative, an equivalent value of cohesion for a

sand layer may be averaged with a cohesion value of

the clay layer as follows:

48

c„ = [ ^ s*K

s*H

s

2*tan$ + (H-Hs)*n'*q

u] /2H.

Where, H = total height of the cut,

Hs

= height of the sand layer,

Y = unit weight of the sand layer,

Ks

= lateral earth pressure coefficient for

the sand layer (~1),

$ = angle of friction of the sand layer,

q = unconfined compression strength of clay,

and

n' = coefficient of progressive failure

(ranges from 0.5 to 1). (Das, 1990)

With the average unit weight for the cut, the

pressure diagrams for clays can then be used to design

the wall. NYCTA (1974) recommends an alternate method

where the pressure diagrams are calculated using

Rankine's earth pressure theory for the individual

layers and an average uniform pressure over the entire

wall calculated from these pressures.

4. Sands are assumed to be drained with the water

table being drawn down below to the bottom of the

excavation. If the cut is not drained or the water

table is not drawn down, the hydrostatic pressure

should be included in the calculations.

49

5. For clays, short-term undrained conditions are

assumed. If drainage may occur as in the cases of

long-term construction (partially drained) or post-

construction (fully drained), an effective stress

analysis should be accomplished using effective stress

parameters (c' and $'). Drained conditions for clays

are usually more critical than undrained conditions.

6. The assumption that the wall acts as a series

of pinned beams is conservative compared to assuming a

continuous beam and analyzing it using a finite

element approach.

7. The program does not calculate the overall

stability of the structure. Most probable failure

surfaces should be checked to ensure a satisfactory

factor of safety.

8. The program does not check the stability of

the base. Seepage forces should also be considered if

present to check for quick conditions.

9. Anchor capacity is based on field testing of

pressure injected tiebacks in cohesionless soils. The

capacity curves used were developed with the majority

of anchors less than eight meters and most were not

tested to their ultimate capacity (FHWA/RD-82/047

,

1982). For cohesive soils, post-grouted tiebacks are

50

assumed. The mechanism by which post-grouted tiebacks

develop their capacity is not entirely understood.

Increases in capacity of 25% to over 300% are possible

depending on the soil type and the post-grouting method

(FHWA-RD-82-047, 1982). The curves used represent a

wide range of values and an average of these values is

used to calculate capacity. The actual field

capacities of the tiebacks should be verified in the

field.

10. Wale design is conservatively calculated based

on assuming pinned ends at the anchor locations.

4.3 Example Problems

Examples problems for sand and clay layering,

with and without a ground water table present are

included in Appendix D. The solutions are compared to

the computer's solutions to ensure reasonable results

are produced by the program.

51

CHAPTER FIVE

USER'S GUIDE

5.1 Program Start-Up

The program may be run either on the computer's

hard drive or one of its floppy drives. From the DOS

prompt, change the command prompt to the drive and

directory on which the program is located. Then type

SOLDIER and press enter to start the program. The

program starts up and displays the main menu shown in

Figure 5.1.

Figure 5.1Main Menu Screen

Design of Soldier Pile and LaggingIn Accordance with NAVFAC DM-7

MAIN MENU1. Enter Soil Properties and Wall Data2. Read Data From an Existing File3. Edit Input Data4. Save Input Data5. Execute Wall Analysis6. Execute Anchor\Wale Analysis7. Save Analysis in an Output File8. Exit Program

Your Choice? --

52

The user then should enter the next step, usually

enter or read data. The description of the required

input data is listed in the next section. The

analysis functions can only be executed after the

data have been entered.

5.2 Input Data

The following data shall be entered for the

various analysis functions. Figure 5.2 illustrates

various input data.

Top Elevat ion

Anchor Elevation

Anchor Elevation

Anchor Elevation

Bottom Elevation

Oistance fro* uall

to strip load

Surcharge Load

Strip Load

Layer ]:

Top elevation, unit ueight, and friction anqle

or cohesion.

Êlevation oi GUT

Lager 2:

Tap elevation, unit ut, and friction angle

or cohesion.

Lager 3:

Top elevation, unit ueiqht, and friction anqle

or cohesion.

Spacing of Soldier Piles

Figure 5.2Input Variables for Wall Analysis

53

5.2.1 Wall Data

1. Name of engineer, for maximum of 40

characters

.

2. Project title, for maximum of 40 characters.

3. Date of report, for maximum of 30 characters.

4. Elevation of the top of the excavation (ft).

5. Elevation of the bottom of the excavation

(ft).

6. Number of anchors used in the cut for a

maximum of ten anchors.

7. Elevation of the anchors from the top of the

excavation to the bottom (ft).

8. Center to center spacing of the soldier piles

(ft).

5.2.2 Soil Data

1. Number of soil layers for a maximum of ten

layers

.

2. Soil type of the entire excavation, either one

for sands or two for clays.

3. For clays, the type of the analysis to be

performed (either total or effective stress analysis)

is entered. If a total stress analysis is to be

accomplished, the saturated unit weight of the soil

54

above and below the ground water table is entered. For

an effective stress analysis, the saturated unit weight

of the soil is entered above the water table and the

buoyant unit weight entered below the water table. The

elevation of the ground water table should be above the

bottom of the excavation for the effective stress

analysis

.

4. Soil properties including elevation of the top

of the layer (ft), saturated, buoyant, or moist unit

weight (kef), and friction angle (degrees) for sands or

undrained shear strength (ksf) for clays.

5. Elevation of the ground water table (ft).

6. Slope of the ground surface behind the

excavation (degrees).

7. Uniform surcharge load (ksf).

8. Strip surcharge load (ksf), the width of the

strip load (ft), and the distance from the wall face to

the start of the strip load (ft).

5.2.3 Wall Analysis Data

1. Estimated width of the flange of the soldier

pile (ft).

2. Factor of safety against passive resistance.

3. Depth of over-excavation below an anchor

elevation for intermediate stages (ft).

55

5.2.4 Anchor Analysis Data

1. The spacing of anchors (ft).

2. The angle of inclination the anchors are set

from horizontal (degrees).

3. The type of soil the anchors are set in. The

options include:

Type Soil Description SPT N Value

1 Fine to medium sand 12 - 30

2 Medium to coarse sand 20 - 45

3 Sandy gravel > 45

4 Medium clay 4-8

5 Medium stiff clay 9-11

6 Stiff clay 12 - 15

7 Stiff to very stiff clay 16 - 20

8 Very stiff clay 21 - 30

9 Very stiff to hard clay > 30

5.3 Output Data

Figure 5.3 lists a typical output file. The

output file is broken down into four sections: wall

properties; soil properties; wall analysis results;

and anchor and wale analysis results. The wall and

soil property sections list the input data for the

wall and soil under items 1 through 12.

56

******************************************************* *

* Design of Soldier Pile and Lagging *

* In Accordance with NAVFAC DM-7 *

* *

******************************************************

I. WALL PROPERTIES1. Engineer: D' Amanda2. Project: International Corporate Park3. Date: 10 November 19894. The elevation of the top of the excavation is

102.00 feet.5. The elevation of the bottom of the excavation is

81.00 feet.6. The number of anchors is 2.

The anchors are located as follows:Anchor Elevation (feet)

1 96.002 89.00

7. The spacing of the soldier piles is 5.00 feet.

II. SOIL PROPERTIES8. The elevation of the water table is 50.00 feet.9. The soil properties are as follows:

Soil Type Elev Unit Wt Friction Angleor Cohesion

sand 102.00 0.1150 38.00

10. The slope of the ground behind the wall is 31.5degrees

.

11. The surcharge load is 0.250 ksf.12. The strip load is 0.50 ksf, 10.00 feet wide, and

located 45.0 feet from the wall.

III. WALL ANALYSIS RESULTS13. Estimated width of the soldier pile is 0.5 feet.14. Factor of safety for passive resistance is 1.0.15. The wall was excavated 1.0 feet below the proposed

anchor location.

Figure 5.3Sample Output File

57

16. STAGE ZERO MAXIMUM SECTION EMBEDMENTREACTION(S)

SHEAR MOMENT MODULUS DEPTH(ft) (k-ft) (iiT3) (ft) (kips)

1 12.1 55.23 23.01 10.12 21.9 20.45 8.52 5.5 Rl = 19.103 17 .0 27 .86 11.61 4.6 Rl = 42.04

R2 = 17.17

NOTE: Stage 1 moment based on Kiewit criteria is42.1 kip-ft.Stage 2 moment based on Kiewit criteria is19.0 kip-ft and reaction force is 16.7 kips.

NOTE: Minimum depth of embedment based on maximummoment is 3.8 feet.

NOTE: NYCTA recommends minimum penetration depth ofsix feet.

IV. ANCHOR AND WALE RESULTS17. Spacing of the anchors is 10.0 feet.18. The anchors are set at an angle of 5.0 degrees.19. The anchors are set in medium to coarse sand.20.ANCHOR SECTION MODULUS ANCHOR ANCHOR UNBONDEDROW OF WALE CAPACITY LENGTH LENGTH

(in"3) (kips) (ft) (ft)

1

2

58.423.8

8434

7.44.0

7.03.8

NOTE: Tieback capacity is based on pressureinjected anchors using and effective groutpressure in excess of 150 psi with a diameterbetween 4 to 6 inches and depth of overburdengreater than 13 feet.

NOTE: FHWA/RD-82/047 recommends a minimum unbondedlength of 15 feet.

END O F ANALYSIS

Figure 5.3 (Continued)Sample Output File

58

In the wall analysis results section, items 13

through 15 are the input values for the width of

the pile, factor of safety for passive resistance,

and the depth of over-excavation respectively. The

actual results from the analysis are listed under

item 16 and include: stage; point of zero shear;

maximum moment; embedment depth; and reaction forces.

The location of the point of zero shear is from the top

of the pile. The depth of embedment is calculated

from the maximum moment for that particular stage and

is measured from the bottom of the cut. Four notes may

be displayed within this section. The results using

the Kiewit criteria for the first two stages are listed

in the first note. The next note lists the minimum

depth of embedment based on the maximum moment from all

stages of excavation. If the penetration depth for the

last stage or the minimum embedment depth is less than

six feet, a note is displayed indicating NYCTA (1974)

recommends a minimum penetration depth of six feet.

The last note is displayed for clay layering stating

the type of analysis, either total or effective stress,

used in the calculations.

The anchor and wale analysis results section

lists the anchor spacing, inclination angle of the

59

anchor, and soil type under items 17 through 19. The

results of the analysis are listed under item 20. It

includes anchor row, section modulus of the wale,

required anchor capacity, (bonded) anchor length, and

unbonded anchor length. A note is displayed stating

how the anchor capacity was derived. Another note is

displayed if the unbonded length of the anchor is less

than fifteen feet. FHWA/RD-82/047 recommends a minimum

unbonded length of fifteen feet.

5.4 Error Messages

The follow error messages are possible within

the program:

"You must input or read data before editing them."

Data must be entered or read before selecting the

edit function.

"You must input or read data before you save

them." Data must be entered or read before selecting

the save data function.

"You must input or read data before analysis ."

Data must be entered or read before selecting the

wall analysis function.

"You must accomplish wall analysis before you can

save it." The wall analysis function must be

accomplished before selecting the save function.

60

"You must accomplish wall analysis before this

analysis ." The wall analysis function must be

accomplished before selecting the anchor/wale analysis

function

.

"The bottom of the excavation must be below the

top." The elevation entered for the bottom of the

excavation must be below the top of the excavation.

"The elevation of this anchor must be below the

prior anchor or the top of the excavation and above the

bottom of the excavation." The elevation entered

for the anchor location must be below the previous

anchor location or the top of the excavation and

above the elevation of the bottom of the excavation.

"The location of the water table can not be above

the top of the excavation." The elevation of the

ground water table must be entered below the elevation

of the top of the excavation.

"The soil type must be either 1 (sands) or 2

(clays)." The soil type for the cut must be entered

either 1 or 2 for sands and clays respectively.

"The first layer must extend to the top of the

excavation." For the first soil layer, the elevation

of the top of the layer must extend to the top of the

excavation.

61

"The elevation of the top of the soil layer must

be below the last layer." The elevation entered for

the top of a soil layer must be below the elevation of

the previous layer.

"The location of the ground water table must be

above the bottom of the excavation for an effective

stress analysis ." When using an effective analysis

approach to calculate stresses for clay layering, the

ground water table must be located above the bottom of

the excavation. The buoyant unit weight of the soil

should be entered below the water table.

"Trouble opening 'filename' -- Read mode. Reenter

the filename or type abort to return to the main menu."

The filename entered for read data does not exist in

the working directory. Either the filename must be

reentered or abort entered to return to the main menu.

"Width must be positive." The estimated width

of the flange of the soldier pile must be entered as

a positive number.

"Factor of safety must be positive." The factor

of safety for passive resistance must be entered as a

positive number.

"Soil will not support the wall below a depth of

XX. X feet." For clay layering, the soil will not

support the wall below the depth listed.

62

CHAPTER SIX

CONCLUSIONS

6.1 Review of Objecti ves

The objective of the computer program was to

provide a rapid and effective method to analyze braced

excavations. By varying the number and location of

tieback anchors, the design of a soldier pile and

lagging wall may be optimized. Once an initial design

is computed, the engineer may then accomplish final

design calculations based on the results from the

computer program. This will significantly reduce the

time to accomplish an actual design.

6.2 Summary of Design Procedures

Recommended design procedures are first to

determine the soil conditions, wall requirements, and

any surcharge loads. Next, select an initial number

of anchors and their respective locations. Then run

the program with the selected data, revising the number

and locations of the anchors until the reaction

forces and required section modulus are within

acceptable limits. A soldier pile section may be

63

selected from the Manual of Steel Construction (1980)

based on the required section modulus. Lagging size

may be chosen from the design table included in chapter

three (Table 3.1) from FHWA/RD-75/124 (1976). The

anchor analysis function of the program may be used to

estimate the wales' section modulus and the unbonded

and bonded length of the tieback anchors. Spacing of

the anchors may be varied until acceptable results are

produced. Also by adjusting the input parameters, the

effects of a ground water table; different soil

conditions; or increased surcharge loading may be

analyzed

.

The program does not check the overall stability

of a wall and the surrounding soil mass. The soil

pressure acting against a wall may be greater in the

case of slope stability than for braced cuts and thus

govern wall design. Also, the factors of safety

against failure of the steel tendons of the anchors

and failure in the anchor zone should be verified

separately. The computer program PCSTABL can be used

to accomplished this analysis.

64

6.3 Conclusions

The program SOLDIER.EXE can provide the engineer

with a quick and effective method of designing a

soldier pile and lagging wall. With the program, the

engineer can also investigate the effects of differing

soil conditions, water table location, surcharge

loading, and wall dimensions and properties.

The engineer must understand the design concepts

and assumptions made within the program to ensure they

are applicable to a particular project. This

computer program is not intended to be a replacement

for a complete design by a competent engineer. The

stresses produced by braced cuts can only be roughly

estimated and a monitoring system should be employed

for critical cuts to ensure the acceptable performance

of the wall. The overall satisfactory performance of

the wall depends greatly on determining accurate soil

parameters, the external loading conditions, and the

use of proper construction procedures.

65

APPENDIX A

VARIABLE NOMENCLATURE

66

The nomenclature of the variables used withinthe program are listed as follow.

Variable

engineer

project

date

telev

belev

numa

anc[10]

s

gwt

nums

soil_type

soil[10][3]

q

bf

Definition (units)

Name of engineer, for maximum of 40characters

.

Project title, for maximum of 40characters

.

Date of report, for maximum of 30characters

.

Top elevation of the excavation (ft).

Bottom elevation of the excavation (ft).

number of anchors used in the cutexcavation.

Elevation of anchor for maximum of tenanchors ( f t )

.

Spacing of the soldier piles (ft).

Elevation of the water table (ft).

Number of soil layers.

Type of soil. Either one for sands ortwo for clays.

Soil properties for maximum of tenlayers: Elevation of top of the layer(ft), saturated or moist unit weight(kef), and friction angle (degrees) orcohesion value (ksf).

Slope of the ground behind theexcavation (degrees).

Surcharge load (ksf).

Estimated thickness of flange of soldierpile (ft).

67

f s Factor of safety against passiveresistance

.

w Depth of over-excavation below theanchor elevation for intermediate stages(ft).

d Spacing of anchors (ft).

ang Inclination angle the anchors are set(degrees )

.

type Soil type for anchor analysiscal culations

.

pi Constant value of 3.141592654.

filename Name of file to save or read data or tosave analysis, for maximum of 10characters

.

wt Average saturated or moist unit weightof cut soi 1 (kef )

.

fa Average Friction angle of soil(degrees)

.

wtb Saturated or moist unit weight of basesoil (ksf )

.

fab Friction angle of base soil (degrees).

Ka Coefficient of active earth pressure forthe cut soil

.

Kab Coefficient of active earth pressure forthe base soil

.

Kp Coefficient of passive earth pressurefor the base soil.

sigh Horizontal stress or force due to soil(ksf or kips )

.

sigs Horizontal stress or force due tosurcharge (ksf or kips).

68

pp Net passive resistance pressure or force(ksf or kips )

.

u Hydrostatic force or stress (kips orksf).

ca Undrained shear strength of cut claysoi 1 (ksf )

.

cb Average undrained shear strength of baseclay soi 1 (ksf )

.

Ns Stability number of the cut for clays.

zt Length of tension zone for clays (ft).

z[ll] Depth of zero shear from top ofexcavation ( f t )

.

R[10][10] Reaction forces for each stage ofconstruction (kips).

M[ll] Maximum moment for a stage of excavation(kip-ft).

S[ll] Required section modulus for a stage ofexcavation (in).

D[ll] Embedment depth for a stage ofexcavation ( f t )

.

Mmax Maximum moment from all stages ofexcavation (kip-ft).

Dmin Minimum embedment depth calculated usingMmax (ft).

Mk[2] Maximum moment from Kiewit Analysis forstage one and two of sand analysis (kip-ft).

Rk Reaction force from Kiewit Analysis forstage two of sand analysis (kips).

P[10] Anchor force for maximum of tenreactions (kips).

69

sw[10] Section Modulus of wale (in )

L[10] Bonded length of anchor (ft).

ul[10] Unbonded length of anchor (ft).

bp Used as a flag.

c Dummy character.

cc[20] Dummy characters, for maximum of twenty

H, h, hh, hhh Various height of the cut variables(ft).

a, v, y Internal variables used in variouscalculations

.

i, j, k, 1 Global counters.

ij, jk Local counters.

str_anal Type of stress analysis to be performedfor clay layering. Either 1 for totalor 2 for effective stress analysis.

70

APPENDIX B

COMPUTER PROGRAM FILE

71

II *************************************************************

// * SOLDIER.EXE, Version 1.01, dtd 15 NOV 91

// * Program written by Kevin D'Amanda.// * Address until Jan 95:

// * COMCBLANT, Naval Amphibious Base Little Creek,// * Norf»4k, VA 23521-5070// *************************************************************

#include <conio.h>#include <stdio.h>#include <ctype.h>include <stdlib.h>include <complex.h>include <string.h>

// **************************************************************// * DECLARE FUNCTION// **************************************************************

void input(void);void read_data( void)void save_data( void)void view_data( void)void analysis( void)

;

void anchor (void)

;

void ka_kp(void);void clay_analysis( void)

;

void wt_c_cb( void)

;

void sand_analysis( void)

;

void save(void);void min_D(void);void strip(void);

// **************************************************************// * DECLARE VARIABLES// **************************************************************

float belev = 0, telev = 0, s = 0, gwt = 0, q = 0, b = 0,anc[10], soil[10][3], hh = 0, H, sw[10], d = 0, ang = 0, L[10],ul[10], bf = 0, fs = 0, w = 0, qs[3];

double sigh, sigs, wt , fa, v, y, Ka , Kp , Kab, wtb, fab, u, P[10],Mc[2], Re, qe, Mmax, Dmin, z[ll], D[ll], M[ll], S[ll],R[10][10], zt, pp, cb, ca, Mk[2], Rk;int type = 0, numa = 0, nums =0, i=0, k=0, j = 0, 1=0,bp = , soil_type, str_anal

;

const float pi = 3.141502654;char c = 'x', cc[20], f ilename[10] , engineer [ 40 ] , project[40],date[30];

72

// **************************************************************

// * MAIN FUNCTION// **************************************************************

main(void) {

// **************************************************************

// * INITIALIZE VARIABLES// **************************************************************

for (i =0; i < 10; i++){ for (k = 0; k < 3; k++) soil[i][k] = 0;

for (j =0; j < 10; j++) R[i][j++] = 0;anc[i] = z[i] = D[i] = M[i] = S[i] = sw[i] = P[i] = ul[i] =

L[i] = 0; }

// **************************************************************// * MAIN MENU ROUTINE// **************************************************************M:clrscr( )

;

cout << "\n"<<<< "\<< "\<< "\<< "\<< "\

coutcout

\tt

t

t

t

t

<<<<<<<<<<<<<<<<

Design of Soldier Pile and LaggingIn Accordance with NAVFAC DM-7

"\n\n\t\t\t MAIN MEN U\n\n";"\t\t 1. Enter Soil Properties and Wall Data\n""\t\t 2. Read Data From an Existing File\n""\t\t 3. Edit Input Data\n""\t\t 4. Save Input Data\n""\t\t 5. Execute Wall Analysis\n""\t\t 6. Execute Anchor\\Wale Analysis\n""\t\t 7. Save Analysis in an Output File\n""\t\t 8. Exit Program\n\n"

W\n'

\n'

\n'\n'

\n'

whilecout<< "

coutswitc

cascascas

elsecoutedit

{

response, try again.

<<<< "\t\t\t Your Choice? -- ";

((i = atoi(gets(cc))) <=0 !! i >=9)<< "\n\t\t" << cc << " is an incorrect\n\a";<< "\t\t\t Your Choice? -- "; }

h (i) {

e 1: input(); bp = 1; break;e 2: read_data(); bp = 1; break;e 3: if (bp) view_data();{ cl rscr( )

;

<< "\n\n\n\tERROR - You must input or read data before youthem!" << "\n\t Press the enter key to return to the

73

main menu. \a";gets(cc); }

break;case 4: if (bp) save_data( )

;

else { clrscr();cout << "\n\n\n\tERROR - You must input or read data before yousave them!" << "\n\t Press the enter key to return tothe main menu.\a";gets(cc); }

break;case 5: if (bp) { analysis(); bp = 2;}

else { cl rscr( )

;

cout << "\n\n\n\tERROR - You must input or read data beforeanalysis!" << "\n\t Press the enter key to return to themain menu. \a"

;

gets(cc); }

break;case 6: if ((bp > 1) && (numa > 0)) anchor();

if (numa == 0) { clrscr();cout << "\n\n\n\t There are no anchors in the wall data,therefore" << "\n\t anchor analysis is not required." <<"\n\n\t Press the enter key to return to the main menu.\a";gets(cc) ; }

if (bp <= 1) { clrscr();cout << "\n\n\n\tERROR - You must accomplish wall analysis beforethis analysis!" << "\n\t Press the enter key to return

to the main menu.\a";gets(cc); }

break;case 7: if (bp > 1) save();

else { clrscr();cout << "\n\n\n ERROR - You must accomplish wall analysis beforeyou can save the data!" << "\n Press the enter to

return to the main menu.\a";gets(cc); }

break;

// *******************************************************// * EXIT ROUTINE// **************************************************************

case 8: cout << "\n\t Are you sure you want to quit the program?(Y/N) -- ";

do { gets(cc);c = toupper(cc[0] )

;

if ((c == 'Y') !! (c == 'N')) break;cout << "\n\tThat's not Yes or No, please enter a Y or N. -- \a";} while (<c != 'Y') ! !

(c != 'N')); }

if (c == 'Y') {

74

clrscr ( ) ;

cout << "\n\n\n\t\tP ROGRAM TERMINATE D\n" ;

exit(O); }

goto M; }

// ***************************************************

// * INPUT FUNCTION// * Enter program variables for calculations.// **************************************************************

void input(void) {

clrscr( )

;

cout << M \n\t\t\tWall Properties\n\n"

;

cout << "\n\tEnter the Engineer's name. -- ";

gets (engineer)

;

cout << "\n\tEnter the project name. -- ";

gets(pro ject )

;

cout << "\n\tEnter the date. -- ";

gets(date)

;

cout << "\n\tEnter the elevation of the top of the excavation infeet. -- ";

cin >> telev;cout << "\n\tEnter the final elevation of the bottom of theexcavation. -- ";

cin >> belev;if (belev >= telev)

{ cout << "\nERROR - The bottom of the excavation must be belowthe top!" << "\n Reenter the final elevation of theexcavation. -- \a";

cin >> belev; }

cout << "\n\tEnter the number of anchors that are to be used tosupport the" << "\n\t excavation for a maximum of ten anchors.

it

.

cin >> numa;if ( numa ) {

cout << "\n\tEnter from the top to bottom the elevation in feetof the anchor(s)

. \n"

;

hh = telev;J = 0;for (1 = 0; 1 < numa; ++1) {

cin >> anc[j];while (anc[j] >= hh || anc[j] <= belev){ cout << "\n\tERROR - The elevation of this anchor must be belowthe prior anchor or" << "\n\t the top of the excavationand above the bottom of the excavation." << "\n\t Reenterthe elevation of this anchor. -- \a";

cin >> anc[j]; }

hh = anc[j]; ++j; } }

cout << "\n\tEnter the spacing of the soldier piles. -- ";

75

cin >> s;

clrscrO;cout << "\n\t\t\tSoil Properties\n\n ;

cout << "\n\tEnter the number of soil layers for a maximum of ten

layers. -- ";

cin >> nums;cout << "\n\tEnter the soil type, either 1 for sands or 2 forclays. -- ";

cin >> soil_type;while ((soil_type <= 0) jj (soil_type >= 3)) (

cout << "\n\n\tERROR - The soil type must be either 1 (sands) or2 (clays). \a M << "\n\t Please reenter soil type. -- ";

cin >> soil_type; }

clrscr ( )

;

if (soil_type == 1) {

cout << "\n\n\tEnter the soil layering properties as follows fromtop down:\n" << "\n\tEl evation of the top of the soil layer infeet from top down." << "\n\tMoist or saturated unit weight ofthe soil (kips/f t~3) .

" << "\n\tFriction angle (degrees)." <<

"\n\t(The entry should read like: 100 .115 35)" <<

"\n\n\tNOTE: The top of the excavation is at elevation " <<

telev << " feet.\n"; }

else {

cout << "\n\n\tDo you wish to perform a total or effective stressanalysis?"

;

cout << "\n\n\tlf you would like to accomplish a TOTAL STRESSANALYSIS enter" << "\n\t the saturated unit weight of the soilabove and below the" << "\n\t ground water table.";

cout << "\n\n\tlf you would like to accomplish an EFFECTIVESTRESS ANALYSIS" << "\n\t enter the satuarted unit weight of thesoil above the water" << "\n\t table and the buoyant unit weightof the soil below the water" << "\n\t table. The water tableelevation should be located above the" << "\n\t bottom of thecut.";

cout << "\n\n\tEnter 1 for a total stress analysis and 2 for aneffective" << "\n\t stress analysis. -- ";

cin >> str_anal

;

while ((str_anal <= 0) !! (str_anal >- 3)) {

cout << "\n\tERROR - Please enter either a 1 (total) or 2

(effective). --\a";cin >> str_anal ; }

clrscr( )

;

cout << "\n\tEnter the soil layering properties as follows fromtop down:" << "\n\tElevation of the top of the soil layer infeet from top down." << "\n\tSaturated or buoyant unit weight ofthe soil (kips/ft~3) ." << "\n\tUndrained shear strength (ksf)."<< "\n\t(The entry should read like: 100 .115 1.5)" <<

"\n\n\tNOTE: The top of the excavation is at elevation " <<telev << " feet.\n"; }

76

ih = 1E10; j = 0;

Eor (i = 0; i < nums; ++i) {

Jin >> soil[j][0] >> soil[j][l] >> soil[j][2];*hile ((soil[j][0] > hh) jj (soil[0][0] != telev))[ if (soil[j][0] > hh)rout << "\nERROR - " << "\n The elevation of the top of thesoil layer must be below the last layer." << "\n Reenterall the soil data for this layer. -- \a";Lf (soil[0][0] != telev)rout << "\nERROR - The first layer must extend to the top of theexcavation" << "\n Reenter all the soil data for thislayer. -- \a";rin >> soil[j][0] >> soil[j][l] >> soil[j][2]; }

in = soil[ j][0] ; ++j; }

: 1 r s c r ( )

;

rout << "\n\tEnter the elevation of the water table in feet. --••

.

rin >> gwt

;

*hile (gwt > telev) {

rout << "\n\nERROR - " << "\n The location of the water table cannot be above the top of the excavation." << "\n Reenter thelocation of the water table. -- \a";rin >> gwt; }

fhile ((str_anal == 2) && (gwt < belev)) {

rout << "\n ERROR - The location of the ground water table mustbe above the bottom" << "\n of the excavation for aneffective stress analysis." << "\n\n Reenter the locationof the water table. -- \a";rin >> gwt; }

rout << "\n\tEnter the slope of the ground behind the wall indegrees. -- ";

rin >> b;rout << "\n\tEnter the surcharge load (ksf)." << "\n\tPleaseenter if none. -- "

;

rin >> q;rout << "\n\tEnter the data for any strip load:" << "\n\tSurcharge load (ksf), width of strip load (ft)," << "\n\t andthe distance the strip load is from the wall (ft)."; cout <<

"\n\tPlease enter 0's if none. -- ";

rin >> qs[0] >> qs[l] >> qs[2];rlrscr(); }

I j **************************************************************

'I * READ DATA FUNCTIONm * Read data from a existing DOS file to enter variables.I / ***************************************************

77

void read_data( void) {

char *cx = "ABORT";cl rscr( ) ;

cout << "\n\n\n\tEnter filename. -- ";

gets( f il ename)

;

FILE *ffp;while ((ffp=fopen(filename,"r"))==NULL) {

printf ( "\nERROR - Trouble opening %s -- read mode.\a",f i 1 ename)

;

cout << "\n\nReenter the filename or type ABORT to return to themain menu. -- ";

gets ( filename)

;

j = strlen( fi 1 ename)

;

for (i = 0; i < j; i++) filename[i] = toupper ( f i 1 ename[ i ] )

;

if (strcmp( fi 1 ename , ex) == 0) break; }

if (strcmp( f i lename, ex) != 0) {

f gets(engineer , 60, ffp);f gets(pro ject , 60, ffp);fgets(date, 30, ffp);fscanf(ffp, "\n %f \n %f \n %f \n %d" , &telev, &belev, &s

,

&numa)

;

for (i = 0; i < numa; ++i){ fscanf(ffp, "\n %f", &anc[i]); }

fscanf(ffp, "\n %f \n %d \n %d \n %d", &gwt, &nums , &soil_type,&str_anal )

;

for (i = 0; i < nums ; ++i){ fscanf(ffp, "\n %f %f %f", &soil[i][0], Ssoil [i] [1]

,

&soil[i][2]);}fscanf(ffp, "\n %f \n %f \n %f %f %f", &b, &q, &qs[0], &qs[l],&qs[2]);fclose(ffp)

;

cout<< "\n\tPlease reenter: Engineer's name. -- ";

gets(engineer ) ;

cout << "\t Project title. -- ";

gets(pro ject ) ;

cout << "\t Date. -- ";

gets(date) ;

cout << "\n\tData read, press enter key to continue.";gets(cc); } }

// ******************************************************// * VIEW AND EDIT ENTERED DATA FUNCTION// * View and edit entered program variables.// **************************************************************

void view_data( void) {

WALL: clrscr();cout << "\n\t\tW ALL PROPERTIE S\n";printf ("\n\tl. Engineer: %s", engineer);

78

rintf ("\n\t2. Project: %s", project);>rintf (

M \n\t3. Date: %s",date);rout << "\n\t4. The elevation of the top of the excavation is

<< telev << " feet." << "\n\t5. The elevation of thebottom of the excavation is " << belev << " feet." << "\n\t6.The number of anchors is " << numa <<".";

f (numa) {

rout << "\n\n\t The anchors are located as follows:\n" <<

"\t\tAnchor" << "\tElevation (feet)\n";j = 0;

for (i = 0; i < numa; + + i)

{ printf("\t\t %2d\t %5.2f\n", ++j, anc[i]);}}cout << "\n\t7. The spacing of the soldier piles is " << s << "

feet.";cout << "\n\n\tDo you want to change any values? (Y/N) -- ";

do { gets( cc)

;

b = toupper ( cc[0 ] )

;

if ((c == 'Y' ) ! !(c == 'N' )) break;

else {

cout << "\n\t" << cc << " is an incorrect response, try again --

\a"; } } while (c !='N' )

;

;if (c == 'N') { SOIL: clrscr();cout << "\n\t\tS OIL PROPERTIE S";cout << "\n\n\t8. The elevation of the water table is " << gwt<< " feet." << "\n\t9. The soil properties are as follow:\n"<< "\n\t Soil Type Elev Unit Wt FrictionAngle" << "\n\\t or Cohesion";

j = 0;for (i = 0; i < nums ; ++i) {

cout << "\n\tif (soil_type == 1) cout << "sand";else cout << "clay";printf (" %7.2f %1.4f %5.2f'\soil[j][0], soil[j][l], soil[j][2]);

j++; >

cout << "\n\n\tl0. The slope of the ground behind the wall is "

<< b << " degrees.";cout << "\n\tll. The surcharge load is " << q << " ksf.";printf ("\n\tl2. The strip load is %7.2f ksf, %4.2f feet wide,",qs[0], qs[l]);printf ("\n\t and located %5.1f feet from the wall.",qs[2]);

cout << "\n\n\n\tDo you want to change any values? (Y/N) -- ";

do { gets(cc)

;

c = toupper(cc[0] )

;

if ((c == 'N' ) ! ! (c == 'Y')) break;else {

cout << "\n\t" << cc << " is an incorrect response, try again --

\a"; } } while (c !='Y' ); }

79

// **************************************************************

// * EDIT DATA ROUTINE// * Edit program variables.// **************************************************************

if (c == 'Y') {

cout << "\n\tEnter the number of what you want to change -- ";

while ((i = atoi(gets(cc) ) ) <= j| i >= 13)

{ cout << "\n\t" << cc << " is an incorrect response . \a"

;

cout << "\n\tYour choice? --";}

clrscr( )

;

switch (i) {

case 1: cout << "\n\tEnter the Engineer's name -- ";

gets( engineer)

;

break;case 2: cout << "\n\tEnter the project name. -- ";

gets(pro ject )

;

break;case 3: cout << "\n\tEnter the date. -- ";

gets(date)

;

break;case 4: cout << "\n\tEnter the elevation of the top of theexcavation in feet. -- \n";

cin >> telev;soil[0][0] = telev;break;case 5: cout << "\n\tEnter the elevation of the bottom of theexcavation in feet. -- "

;

cin >> be lev;break;case 6:

cout << "\n\tEnter the number of anchors that are to be used. --M .

I

cin >> numa;hh = 0;i f ( numa ! = )

{ J = 0;cout << "\n\tEnter from the top to bottom the elevation in feetof the anchor(s) --\n";

for (1 = 0; 1 < numa; ++1){ cin >> anc[j];hh = telev;while (anc[j] >= hh |j anc[j] <= belev) {

cout << "\n\tERROR- The elevation of this anchor must be belowthe prior anchor or" << "\n\t the top of the excavationand above the bottom of the excavation." << "\n\n\tReenter theelevation of this anchor. -- \a";

cin >> anc[j]; }

hh = anc[j]; ++j; } }

80

break;C 3 S 6 V t

cout << "\n\tEnter the spacing of the soldier piles. -- ";

c i n > > s ;

c 1 r s c r ( ) ;

break

;

case 8: cout << "\n\n\tEnter the elevation to the water table in

feet. -- ";

cin >> gwt ;

if (gwt > telev) {

cout << M \nERROR - " << "\n The location of the water table cannot be above the top of the excavation." << "\n Reenter thelocation of the water table -- \a";

cin >> gwt; }

break;case 9: cout << "\n\tEnter the number of soil layers. -- ";

cin >> nums;cout << "\n\tEnter the soil type, either 1 for sands or 2 forclays. -- ";

cin >> soil_type;while ((soil_type <= 0) |j (soil_type >= 3)) {

cout << "\n\tERROR - The soil type must be either 1 (sands) or 2

(clays)." << "\n\t Please reenter soil type. -- \a";cin >> soil_type; }

if (soil_type == 2) {

cout << "\n\tDo you wish to perform a total or effective stressanalysis?" << "\n\tEnter 1 for a total stress analysis and2 for an effective" << "\n\t stress analysis. -- ";

cin >> str_anal

;

while ((str_anal <= 0) || (str_anal >= 3)) {

cout << "\n\tERROR - Please enter either a 1 (total) or 2

(effective). --\a"; cin >> str_anal; } }

cout << "\n\tEnter the soil layer's properties:" <<"\n\tElevation of top of the layer, unit weight, and frictionangle" << "\n\t or undrained shear strength. \n"

;

hh = 1E8; j = 0;for (1=0; 1 < nums; ++1) {

cin >> soil[j][0] >> soil[j][l] >> soil[j][2];while ((soil[j][0] > hh) !! (soil[0][0] != telev)){ if (soil[j][0] > hh)cout << "\nERROR - " << "\n The elevation of the top of thesoil layer must be below the last layer." << "\n Reenterall the soil data for this layer. -- \a";

if (soil[0][0] != telev)cout << "\nERROR - The first layer must extend to the top of theexcavation" << "\n Reenter all the soil data for thislayer. -- \a";

cin >> soil[j][0] >> soil[j][l] >> soil[j][2]; }

hh = soil[j][0]; ++j; }

81

break;case 10: cout << "\n\tEnter the slope of the ground behind thewall in degrees. -- ";

c i n > > b ;

break

;

case 11: cout << "\n\tEnter the surcharge load (psf)." <<

"\n\n\t\tPl ease enter if none. -- "

;

c i n > > q

;

break;case 12:cout << "\n\tEnter the data for any strip load:" << "\n\tSurcharge load (ksf), length of strip load (ft)," << "\n\t andthe distance the strip load is from the wall (ft).";

cout << "\n\tPlease enter if none. -- ";

cin >> qs[0] >> qs[l] >> qs[2];break; }

cl rscr ( )

;

if (i < 8) goto WALL;else goto SOIL; } }

// **************************************************************// * SAVE DATA FUNCTION// * Save entered data into a DOS file.// **************************************************

void save_data( void) {

FILE *fp;clrscr ( )

;

cout << "\n\tEnter filename to save the data. -- "

;

gets( f i lename)

;

while ((fp=fopen(filename,"r") ) != NULL) {

cout << "\n\tThe file already exits, do you want to overwrite it?(Y/N) -- \a";

gets( cc)

;

c = toupper ( cc[0] ) ;

switch (c) {

case '

Y' : break

;

case 'N': cout << "\n\tReenter the filename. -- "

;

gets( f i lename)

;

break;default :

cout << "\n\t" << cc << " is an incorrect response, try again.-- \a";

gets(cc)

;

c = toupper ( cc[0 ]) ; }

if (c == 'Y') { c = 'x' ; break; } }

fp = fopen( filename, "w+");fprintf(fp, "%s", engineer);fprintf(fp, "\n %s", project);

82

%f%dnuma%f"%d M

%d"%d"nums

"\n %f %f %f"\n %f", b)

;

"\n %f", q);"\n %f %f %f

"\n"\nJ <

"\n"\n"\n"\ni <

date)

;

telev)belev)s);numa)

;

+ + j)gwt) ;

nums )

;

soi l_type)

;

str_anal )

;

+ + i)

fprintf (fp, "\n %f", anc[ j])

;

soil[i][0], soil[i][l], soil[i][2]);

qs[0], qs[l], qs[2]);

main

fprintf(fp, "\n %s"fprintf(fp, "\n %f"fprintf(fp, "\n %f"fprintf ( f p,f printf ( f p,for (j = 0;fprintf ( f p

,

fprintf ( f p,fprintf ( f p,fprintf ( fp,for (i = 0;fprintf ( f p,fprintf ( fp,fprintf ( f p,fprintf ( f p

,

f close( f p)

;

cout << M \n\tData saved, press enter key to return themenu .

"

;

gets( cc)

;

cl rscr( ) ; }

// ***************************************************

// * ANALYSIS FUNCTION// * Determine soil type, call subfunction to accomplish// * calculations, and display results from analysis.// **************************************************************

void analysis( void) {

cl rscr ( )

;

// Enter Width of Pile, Factor of Safety, & Excav. Depthcout << "\n\n\tEnter the estimated width of the flange of thesoldier pile." << "\n\t (Enter for default setting of 1

foot. ) -- ";

cin >> bf

;

if (bf < 0){ cout << "\n\tERROR - Width must be positive, Reenter width --

\a";cin >> bf;}if (bf == 0) bf = 1;cout << "\n\n\tEnter the factor of safety for the passivepressure." << "\n\t(Enter for DM-7 recommendation of 1.5.)

ii

.

cin >> fs;if (fs < 0){ cout << "\nERROR - Factor of safety must be positive, ReenterF.S. -- \a";

cin >> fs; }

if (fs == 0) fs = 1.5;if (numa) {

83

cout << M \n\n\tEnter the depth in feet below the anchor locationthat is to " << "\n\t excavated prior to installing theanchor. -- "

;

cin >> w; }

cl rscr ( )

;

cout <<"\n\n\n\t\t\tC A L C U L A T I N G ";

if (soil_type == 1) sand_anal ysis ( )

;

if (soil_type == 2) cl ay_anal ysis ( )

;

if (z[0] >= 0) { i = 1, j = 0;

cl rscr ( )

;

cout << "\n\n\tRESULTS: " << " \n\n\ tEst imated width of the soldierpile is " << bf << " feet.";

cout << "\n\tFactor of Safety for passive resistance is " << fs<< ".";

cout << "\n\tThe wall was excavated " << w << " feet below theproposed anchor location.";

cout << "\n\n\t STAGE ZERO MAXIMUM SECTION EMBEDMENTREACTION(S)" << "\n\t SHEAR MOMENT MODULUS

DEPTH" << "\n\t (ft) (k-ft) (iiT3)(ft) (kips)" << "\n\t

printf( "\n\t %d %6.1f %6.2f %6.2f %6.1f---", i, z[i-l], M[i-1], S[i-1], D[i-1]);

for (i = 2; i <= numa + 1; ++i) {

printf( "\n\t %d %6.1f %6.2f %6.2f %6.1f Rl =

%6.2f", i, z[i-l], M[i-1], S[i-1], D[i-1], R[0][j]);for (k = 2; k <= nurna; + + k) {

if (R[k-l][j]) {

cout << "\n\t\t\t\t\t\t\t R" << k << " = ";

printf("%6.2f", R[k-l][j]); } } + + j; }

printf ( "\n\nNOTE: Stage 1 moment based on Kiewit criteria is%6.1f kip-ft.", Mk[0]);

if (numa > 0) {

printf("\n Stage 2 moment based on Kiewit criteria is %6.1fkip-ft", Mk[l]);

printf("\n and reaction force is %6.1f kips.", Rk); }

if (numa > 1) printf ( "\nNOTE : Minimum depth of embedment basedon maximum moment is %3.1f feet.", Dmin);

if ((D[numa] < 6) !! (Dmin < 6)) {

cout << "\nNOTE: NYCTA recommends minimum penetration depth ofsix feet."; } }

if ((soil_type == 2) && (str_anal == 1))printf ("\nNOTE: A total stress analysis approach was used.");if ((soil_type == 2) && (str_anal == 2))printf ("\nNOTE: An effective stress analysis approach wasused.");cout << "\n\nPress the enter key to return to the main menu. ";

gets(cc); }

84

\l I**************************************************************

// * SAND ANALYSIS FUNCTION// * Execute analysis for sands// *************************************************************

void sand_analysis(void) {

// *************************************************************

// * STAGE I - SAND// *************************************************************

j=0; i=0; v=0; y = 0;

if (numa) hh = anc[j] - w;else hh = belev;

!ka_kp();strip( )

;

ihh = telev - hh;sigh = Ka*wt*hh*s*hh/2; // Horizontal Stress due to Soilsigs = Ka*qe*s*hh; // Horizontal Stress due to Surchargepp = (3*Kp/fs-Kab)*bf*wtb;z[0] = 0; /* Zero Shear */

u = 0;while(sigh + sigs + Kab*(wt*hh+qe)*bf *z[0] - pp*z [0 ] *z [0 ]/2 + u > 0){ z[0] = z[0] + 0.05;if (gwt >= (telev - hh ) ) u = . 0312*bf *( 3*Kp/f s-Kab)*z[0]*z [0]

;

else u=0; }

if ( (gwt > telev - hh - z[0]) && (gwt < telev - hh) )

{ z[0] = 0;while (sigh + sigs + Kab*( wt*hh+qe)*bf *z [0 ] - pp*z[0]*z[0 ]/2 +

0.0312*bf*(3*Kp/fs-Kab)*(z[0]-telev+hh+gwt)*(z[0]-telev+hh+gwt)>0) z[0]=z[0]+0.05;}

v = z[0]; /* Calculate Maximum Moment */ if(gwt <= (telev - hh - z[0])) u = 0;else{ if (gwt >= telev - hh) u = . 0104*bf *( 3*Kp/f s-Kab)*v*v*v;else u = 0.0104*bf*(3*Kp/fs-Kab)*pow((v-telev+hh+gwt),3); }

M[0] = sigh*(hh/3+v)+ sigs*(hh/2+v)+ Kab*bf *(hh*wt+qe)*v*v/2-pp*v*v*v/6+ u;S[0] = M[0]/2.4; /* Calculate Section Modulus */v = 0; /* Calculate Depth of Embedment */u = 0;while (sigh*(hh/3+v)+sigs*(hh/2+v)+Kab*bf*(wt*hh+qe)*v*v/2-pp*v*v*v/6+u > 0) { v = v + 0.05;if (gwt >= (telev - hh ) ) u = . 0104*bf *( 3*Kp/f s-Kab)*v*v*v;else u = 0; }

if ((gwt > telev - hh - v) && (gwt < telev - hh) ) { v = 0;while (sigh*(hh/3+v)+ sigs*(hh/2+v) + Kab*bf *(hh*wt+qe)*v*v/2-pp*bf*v*v*v/6 + 0.0104*bf*(3*Kp/fs-Kab)*pow( (v-telev+hh+gwt) ,3)

85

> ) v =v+0.05; }

D[0] = v;

z[0] = hh + z[0];// Calculate Moment based on Kiewit Analysis

Mk[0] = Ka*qe*hh*s*(hh/2+2)+Ka*wt*hh*hh*s*(hh/3+2)/2; Dmin = 7;

cout << "\n\n\t\t STAGE 1 COMPLETED.";it **************************************************************

II * STAGE II - SANDS// **************************************************************

if (numa) { ++i

;

j = 1; v = 0; y = 0;if (numa == 1) hh = be lev;

else hh = anc[j] - w;

ka_kp( )

;

strip( )

;

hh = telev - hh;sigh = Ka*wt*s*hh*hh/2; /* Horizontal Stress due to Soil*/ sigs = Ka*qe*s*hh; /* Horizontal Stress due toSurcharge */ pp = ( 3*Kp/f s-Kab) *wtb*bf

;

v = 0;u = 0;while (sigh + sigs + Kab*(hh*wt+qe) *bf *v - pp*v*v/2 + u > 0) {

v = v + 0.05;if (gwt >= (telev - hh ) ) u = . 0312*bf * ( 3*Kp/f s-Kab)*v*v;else u=0; }

if ( (gwt > telev - hh - v) && (gwt < telev - hh) )

{ v = ; u = ;

while (sigh + sigs + Kab*(hh*wt+qe) *bf *v - pp*v*v/2 +

0.0312*bf*(3*Kp/fs-Kab)*(v-telev+hh+gwt)*(v-telev+hh+gwt) > 0)v = v + 0.05; }

/* Reaction Force */

if (gwt <= (telev - hh - v)) { u = 0; }

else{ if (gwt >= telev - hh) { u = . 0104*bf *( 3*Kp/f s-Kab)*v*v*v; }

else { u = 0.0104*bf*(3*Kp/fs-Kab)*pow((v-telev+hh+gwt) ,3) ; } }

R[0][0] = (sigh*(hh/3+v)+ sigs*(hh/2+v) + Kab*(wt*hh+qe)*bf *v*v/2- pp*v*v*v/6 + u) / (hh+anc[0

]

-telev+v) ;

v = 0; u = 0; /* Zero Shear */while (R[0][0] - sigh - sigs - Kab* ( wt*hh+qe)*bf *v + pp*v*v*bf/2-u<0) {v=v+0.05;

if (gwt >= (telev - hh ) ) u = . 0312*bf *( 3*Kp/fs-Kab)*v*v;else u=0; }

if ( (gwt > telev - hh - v) && (gwt < telev - hh) ) { v = 0;while ( R[0][0] - sigh - sigs - Kab* ( wt*hh+qe) *bf *v + pp*v*v*bf/2- 0.0312*bf*(3*Kp/fs-Kab)*(v-telev+hh+gwt)*(v-telev+hh+gwt) < 0)

v = v + 0.05; }

z[l] = v;

86

if (gwt <= (telev - hh - v ) ) { u = ; } // Maximum Momentelse{ if (gwt >= telev - hh) u = . 0104*bf * ( 3*Kp/ f s-Kab) *v*v*v ;

else u = .0104*bf *( 3*Kp/ f s-Kab) *pow( ( v- te 1 ev+hh+gwt ) , 3 ) ; }

M[l] = sigh*(hh/3+z[l]) + sigs* ( hh/ 2 + z [ 1 ] ) +

Kab*(wt*hh+qe)*bf*z[l]*z[l]/2 - pp*z[ 1] *z[ 1

] *z[ 1 ]/6 -

R[0][0]*(hh-telev+anc[0]+z[l]) + u; S[l] = M[l]/2.4;// Section ModulusD[l] =0; u = 0; /* Depth of Embedment */

while (M[l] - Ka*(qe+(telev-anc[0] )*wt)*pow( (hh-telev+anc[0]) ,2)*s/2 - s*Ka*wt*pow( (hh- tel ev+anc[0 ] ) , 3 ) / 3 -

bf*Kab*(qe+hh*wt)*D[l]*(D[l]/2+hh-telev+anc[0] ) +

pp*D[l]*D[l]/2*(2*D[l]/3+hh-telev+anc[0]) - u < )

{ D[l] = D[l] + 0.05;if (gwt >= (telev - hh ))

u = 0.0312*bf*(3*Kp/fs-Kab)*D[l]*D[l]*(2*D[l]/3+hh-telev+anc[0])

;

else u=0; }

if ((gwt > telev - hh - D[l]) && (gwt < telev - hh) ) { D[l] = 0;

while ( M[l] - Ka*(qe+(telev-anc[0] )*wt)*pow( (hh -

telev+anc[0]) ,2)*s/2 - s*Ka*wt*pow( (hh-tel ev+anc[0 ] ) , 3)/3+ pp*D[l]*D[l]/2*bf*(hh-telev+anc[0]+2*D[l]/3) -

bf*Kab*(qe+hh*wt)*D[l]*(D[l]/2+hh-telev+anc[0]) -

0.0312*bf*(3*Kp/fs-Kab)*pow((D[l]-telev+hh+gwt) ,2)*(D[l]+hh-telev+anc[0]-(D[l]-telev+hh+gwt)/3) < 0)

D[l] = D[l] + 0.05; }

z[l] = z[l] + hh;// Calculate Moment & Reaction based onKiewit y = hh-tel ev+anc[0 ]

;

Mk[l] = Ka*s*y*y*(qe+wt/2*(hh+telev-anc[0]))/9;Rk = Ka*qe*s*(telev-anc[0] ) + Ka*wt*s*pow( ( telev-anc[0] ) , 2 )/2 +

(Ka*s*y*y/2*(qe+wt*(telev-anc[0] ) ) + y*y*y*Ka*s*wt/6)/y

;

cout << "\n\t\t STAGE 2 COMPLETED.";}/I *******************************************************// * STAGE III - SANDS/ / **************************************************************

J = 2;while (j <= numa) {

v = 0; y = 0; /* Average Unit Wt & FricionAngle */ if (j < numa) hh = anc[j] - w;else hh = be lev;

ka_kp();strip( )

;

sigs = Ka * qe; /* Horizontal Stress due to Surcharge */

sigh = 0.65 * Ka * wt * (telev - hh);/* Horizontal Stress due to Soil */for (i = 0; i < 10; i++) { R[i][j-1] = 0; }

for (k = 0; k < j; ++k) /* Calculate Reaction Forces */

87

{ if (k < j - 1) H = anc[k+l];else H = hh;v = 0;for ( i = 1; i <= k; ++i) v = R[i-l][j-l] * (anc[i-l] - H) + v;

R[k][j-1] = (pow((telev-H) , 2) * ( sigh+sigs ) *s/ 2 - v) / (anc[k]-H);

} i = 0;

// Calculate point of Zero Shearv = R[0][j-1];while (v - (telev - anc[i]) * (sigh + sigs) * s > )

{ v = R[++i][j-l] + v;

if (i == j - 1) break; }

z[j] = v / ((sigh + sigs) * s);v = 0; /* Calculate Maximum Moment */

i = 0; M[j] = 0;

while (telev - anc[i] < z [ j ]

)

{ v = R[i][j-1] * (z[j] - telev + anc[i]);+ + i;

M[j] = M[j] + v;

if (i == j) break; }

M[j] = M[j] - (sigh + sigs) * s * z[j] * z[j] / 2;

S[j] = M[j]/2.4;/* Calculate Depth of Embedment */

v = M[j]; min_D(); D[j] = y;if (j == numa) { Mmax = M[0];for (i = 1; i <= numa; i + +) if (M[i] > Mmax) Mmax = M[i];v = Mmax; min_D( ) ; Dmin = y; }

++j;cout << "\n\t\t STAGE " << j << " COMPLETED.";} }

// ****************************************************// * CLAY ANALYSIS FUNCTION// * Execute analysis for clays./ / **************************************************************

void clay_analysis( void) {

fa = 0; j = 0;

// **************************************************************// * STAGE I - CLAYS// *************************************************************

if (numa) hh = anc[0] - w;else hh = belev;

float hhh = telev - hh;wt_c_cb( ) ; /* Calculate Average unit wt , c, and c base */strip();zt = ( 2*ca-qe)/wt ; /* Depth of Tension Zone */if ((6/fs*cb+2*cb-qe-wt*(telev-hh) < 0))

88

{ v = (6*cb/fs+2*cb-qe)/wt

;

printf ( "\a\n\n\nERROR - Soil will not support the wall below a

depth of %4.2f feet.", v) ;

z[0] = -1; goto Q; }

if ((hh >= telev - zt) && (zt >= 0)){ M[0] = 0; z[0] = 0; S[0] = 0; D[0] = 0; }

if ((hh < telev - zt) && (zt >= 0)) {

sigh = s*(wt*hhh+qe-2*ca)*(hhh-zt )/2 ; /* Active Pressure */

pp = ( 6*cb/fs+2*cb-wt*hhh-qe)*bf ; // Result. Resistance Press.z[0] = sigh / pp; /* Zero Shear */

M[0] = sigh*( (hhh-zt )/3+z[0 ] ) - PP*z [0 ] *z [ ] / 2 ; // Max. MomentD[0] = 0; /* Depth of Embedment */

while (sigh*( (hhh-zt )/3+D[0 ]) -pp*D[0 ] *D[0 ]/2 > 0) D[0] = D[0] +

0.05;z[0] = z[0] + hhh; }

if ( zt < 0) {

pp = (6*cb/fs+2*cb-wt*hhh-qe)*bf /* Resultant Resist Pres */

z[0] = ((qe-2*ca)*hhh*s + wt*hhh*hhh/2*s ) / pp; /* Zero Shear */

// Max. MomentM[0] = (qe-2*ca)*hhh*s*(hhh/2+z[0])+wt*hhh*hhh/2*s*(hhh/3+z[0])-pp*z[0]*z[0]/2;

D[0] = 0; /* Depth of Embedment */while (s*(qe-2*ca)*hhh*(hhh/2+D[0] ) + wt*hhh*hhh/ 2*s* (hhh/ 3+D[0 ]

)

- pp*D[0]*D[0]/2 > 0) D[0] = D[0] + 0.05;z[0] = z[0] + hhh; }

S[0] = M[0]/2.4;// Kiewit AnalysisMk[0] = 0;if (zt < 0) Mk[0] = s*wt*hhh*hhh/2*(hhh/3+2) +

s*(qe-2*ca)*hhh*(hhh/2 + 2) ;

if ((zt >= 0) && (zt < hhh))Mk[0] = s*(wt*hhh+qe-2*ca) * (hhh-zt)/2 *

( (hhh-zt )/3+2 )

;

Dmin = 7; Kp = zt;// Set zt, stage 1 equal to Kp to compare to zt, stage 2

cout << "\n\n\t\t STAGE 1 COMPLETED.";// ****************************************************// * STAGE II - CLAYS// **************************************************************

if (numa) {

j = i;if (numa == 1) hh = be lev;

else hh = anc[l] - w;wt_c_cb( )

;

strip()

;

zt = (2*ca-qe)/wt;if (zt > Kp) zt = Kp;hhh = telev-hh;

89

if ((6/fs*cb+2*cb-qe-wt*(telev-hh) < 0))

{ v = (6*cb/fs+2*cb-qe)/wt;printf ( "\a\n\n\nERROR - Soil will not support the wall below a

depth of %4.2f feet.", v);z[0] = -1; goto Q; }

if ((hh > telev - zt) && (zt >= 0))

{ M[l] = 0; z[l] = 0; R[0][0] = 0; S[l] = 0; D[l] = 0; Re - 0;

Mc[l] = 0; }

if ((hh < telev - zt) S.& (zt >= 0)) {

hh = telev - hh;sigh = s*(wt*hh+qe-2*ca)*(hh-zt)/2;pp = (6*cb/fs+2*cb-wt*hh-qe)*bf

;

v = sigh / pp; /* Zero Earth Forces */

R[0][0] = (sigh*((hh-zt)/3+v) - pp*v*v/2) / ( hh- tel ev+anc[ ] +v )

;

z[l] = (sigh - R[0][0]) / pp; /* Zero Shear */

M[l] = sigh*((hh-zt)/3+z[l]) - pp*z [ 1] *z [ 1 ]/2 - R[0][0]*(hh

-telev+anc[0]+z[l]) ; D[l] = 0;

if (anc[0] > telev-zt) {

while (M[l] + pp*D[l]*(D[l]/2+hh-telev+anc[0] ) - sigh *

(hh+anc[0]-telev-(hh-zt)/3) < 0)D[l] = D[l] + 0.05; }

else {

while (M[l] + pp*D[l]*(D[l]/2+hh-telev+anc[0]) -

s*(qe-2*ca+wt*(telev-anc[0] ))* pow( (hh-telev+anc[0 ] ) , 2 )/2 -

s*wt*pow( (hh-telev+anc[0]) ,3)/3 < 0)D[l] = D[l] + 0.05; }

z[l] = z[l] + hh; }

if (zt < 0) { hh = telev - hh;pp = (6*cb/fs+2*cb-wt*hh-qe)*bf

;

sigh = s*wt*hh*hh/2;sigs = s*(qe-2*ca)*hh;v = (sigh + sigs) / pp;R[0][0] = (sigh*(hh/3+v) + sigs*(hh/2+v) - pp*v*v/2) / (hh-telev+anc[0 ]+v)

;

z[l] = (sigh + sigs - R[0][0]) / pp;M[l] = sigh*(hh/3+z[l]) + sigs*(hh/2+z[ 1 ] ) - pp*z[l]*z[l]/2 -

R[0][0]*(hh-telev+anc[0]+z[l]);D[l] = 0;while (M[l] + pp*D[l]*(D[l]/2+hh-telev+anc[0]) -

s*(qe-2*ca+wt*(telev-anc[0])) * pow( (hh-telev+anc[0 ] ) , 2 )/2 -

s*wt*pow((hh-telev+anc[0]),3)/3 < 0) D[l] = D[l] + 0.05;z[l] = z[l] + hh; }

S[l] = M[l]/2.4;

H = hhh-zt; // Kiewit Analysisv = telev - anc[0];y = hhh-telev+anc[0]

;

Mk[l] = Rk = 0;if (zt < 0) { Mk[l] = s*y*y*(qe - 2*ca + wt*v + wt*y/2)/9;

90

Rk = s*(qe-2*ca)*v + s*wt*v*v/2 +

s*((qe-2*ca +wt*v)*y/2 +wt*y*y/6) ; }

if (((zt >= 0) && (zt >= y)) && (zt < hhh)) {

Mk[l] = s*y*y/9 * (qe-2*ca + wt*hhh)*H/(2*y) ;

Rk = s*(wt*hhh+qe-2*ca)*H*H/(6*y) ; }

if ( (zt > = 0) && (zt < y) ) {

Mk[l] = s*y*y/9 * (qe - 2*ca + wt*v + wt*y/2);Rk = s*( (qe-2*ca+wt*v)*(v-zt)/2 +

( qe- 2*ca+wt*v ) *y/ 2 + wt*y*y/6);} cout << "\n\t\t STAGE 2 COMPLETED."; }

/ / *********************************************************// * STAGE III - CLAYSII **************************************************************

if (numa > 1) {

J = 2;

while (j <= numa) {

double a, h;

if (j < numa) hh = anc[j] - w;

else hh = belev;wt_c_cb( )

;

strip( ) ;

if ((6/fs*cb+2*cb-qe-wt*(telev-hh) < 0)){ v = (6*cb/fs+2*cb-qe)/wt;printf ( "\a\n\n\nERROR - Soil will not support the wall below a

depth of %4.2f feet.", v)

;

z[0] = -1; goto Q; }

float Ns = wt*(telev-hh)/ca; /* Stability Number */

for (i = 0; i < 10; i + + ) R[i][j-1] = 0;for (k = 0; k < j; k++) {

if (k < j - 1) H = anc[k+l]

;

else H = hh;h = telev - hh;a = telev - H;v = 0;if (gwt > H) u = 0.0104*pow( (gwt-H) ,3)*s;else u = ;

for (i = 1; i <= k; i++) v = R[i-l][j-l] * (anc[i-l] - H) + v; if(Ns <= 6)

{ if (a < h/4) sigh = 1 . 6*wt*pow( a , 3 )/6;if ((a >= h/4) && (a <= 3*h/4))sigh = 0.05*wt*h*h*(a-h/6) + . 2*wt*h*pow( (a-h/4) , 2 )

;

if (a > 3*h/4) sigh = wt*pow(h, 2) *(0 . 05*(a-h/6) + 0.2*(a-h/2))

+ 0.4*wt*pow((a-.75*h) ,2)*(h-2*a/3); }

if (Ns > 6){ Ka = 1 - 4*ca/(wt*h);if (a < h/4) sigh = 2*Ka*wt*a*a*a/3

;

else sigh = Ka*wt*h*h/8*( a-h/6 ) + Ka*wt*h*pow( (a-h/4) , 2 )/2 ; }

R[k][j-1] = (s*qe*pow((telev-H) ,2)/2 + s*sigh - v + u) /

91

(anc[k]-H); }

v = 0; /* Calculate point of Zero Shear */

u = 0; z[j] = 0;

for (i = 0; i < numa; i++) v = R[i][j-1] + v;

if (Ns <= 6) {

while ( v + .05*wt*h*h*s -( qe+0 . 4*wt *h) *s*z [ j ] - u > 0) {

z[j] = z[j] + 0.05;if (telev - z[j] <= gwt) u = . 0312*s*pow( ( z [ j

] - 1 el ev + gwt ) , 2 ) ; }}

if (z[j] > 3*h/4) {

while (v- s*qe*z[j] -u - s* ( . 25*wt*h*h+ wt * ( h-0 . 8*z [ j ] )*

(z[j]-0.75*h)) > 0)

{ z[j] = z[j] + 0.05;if (telev-z[j] <= gwt)u = 0.0312*s*pow( (z[ j] - telev + gwt ) , 2 ) ; } }

if (Ns > 6) {

while ( v + s*Ka*wt*h*h/8 - s* (Ka*wt*h+qe) *z [ j ] - u > 0){ z[j] = z[j] + 0.05;if (telev-z[j] <= gwt) u = . 0312*s*pow( ( z [ j

] -telev+gwt ) , 2 ) ; } }

v = 0; /* Calculate Maximum Moment */

M[j] = 0;for (i = 0; i < j; + + i)

{ v = R[i][j-1] * (z[j] - telev + anc[i]);M[j] = M[j] + v; }

if (Ns <= 6) {

if (z[j] <= 3*h/4) sigh = . 05*wt*h*h*( z [ j ]-h/6) +

0.2*wt*h*pow((z[ j]-h/4) ,2);else sigh = . 05*wt*h*h*( z [ j] -h/6 ) + . 2*wt*h*h*( z [ j

] -h/2 ) +

0.4*wt*pow( (z[j]-.75*h),2)*(h-2*z[j]/3); }

else sigh = Ka*wt*h*h/8* ( z [ j ]-h/ 6) + Ka*wt*h*pow( ( z[

j

]-h/4) , 2 ) /2

;

if (gwt > telev-z[j]) u = . 0104*s*pow( ( z[ j] -telev+gwt ), 3)

;

else u = ;

M[j] = M[j] - qe*s*z[ j]*z[ j]/2 - sigh*s - u;S[j] = M[j]/2.4;D[j] = 0; /* Calculate Depth of Embedment */

if (Ns <= 6) {

if (anc[j-l] >= telev-3*h/4)sigh = 0.4*wt*h*pow(( . 75*h-telev+anc[ j-1]) ,2)/2 +

0.05*wt*h*h*(5*h/6-telev+anc[ j-1]);else sigh = . 8*wt*(h-telev+anc[ j-1 ] )

*

pow( (h-telev+anc[ j-1] ) , 2)/3; }

else sigh = Ka*wt*h*pow( ( anc[ j-1 ] -hh) , 2 )/2

;

if (gwt >= anc[j-l])u = 0.0312*(gwt-anc[ j-1] )*pow((anc[ j-l]-hh) ,2)*s +

0.0208*pow((anc[ j-l]-hh) , 3 )*s

;

if ((gwt > hh) && (gwt < anc[j-l]))u = 0.0312*pow( (gwt-hh) ,2)*(anc[ j-1] -hh- (gwt-hh)/3)*s

;

if (gwt <= hh) u = 0;while (M[j] + (6*cb/fs+2*cb-qe)*bf*D[ j]*(D[ j]/2+(anc[ j-l]-hh)) -

sigh*s - s*qe*pow((anc[ j-l]-hh) ,2)/2 - u < 0)

92

D[ j] = D[ j] + 0.05;+ + j;cout << "\n\t\t STAGE " << j << " COMPLETED. ";}}if (numa > 1) { Mmax = M[0];for (i = 1; i <= numa; i++)if (M[i] > Mmax) Mmax = M[i]; Dmin = 0;

while (Mmax + ( 6*cb/

f

s+2*cb-qe ) *bf *Dmin* ( Dmin/ 2 + ( anc [j

- 2]

- hh )

)

- sigh*s - s*qe*pow( (anc[ j-2 ] -hh) , 2 )/2 - u < 0)Dmin = Dmin + 0.05; } Q: i = 0; }

it **************************************************************

// * KA_KP FUNCTION// * Cal . average unit weight, friction angle, and Ka for cut.// * Calculate unit weight, friction, Ka , and Kp for base soil.// ********************************************************

I

void ka_kp(void) {

for (k = 0; hh < soil [k+1] [0] ; + + k)

{ if (k >= (nums-1)) break;v = soil[k][l] * (soil[k][0] - soi 1 [k+1] [0 ] ) + v;

y = soil[k][2] * (soil[k][0] - soi 1 [k+1 ] [0 ] ) + y; }

v = v + soil[k][l] * (soil[k][0] - hh);y = y + soil[k][2] * (soil[k][0] - hh) ;

wt = v / (telev - hh)

;

fa = y / (telev - hh);1 = nums - 1

;

while (hh > soil[l][0]) — 1;fab = soil[l][2];wtb = soil[l][l];Kp = pow(tan((45 + f ab/ 2

) *pi/ 180 ) , 2 ) ; /* Calculate Ka & Kp */

Kab = pow(tan((45 - f ab/2 ) *pi/180 ) , 2 )

;

if (b == 0) { Ka = pow(tan((45 - f a/2 )*pi/180) , 2) ; }

else { Ka = pow(cos( f a*pi/180 ) , 2 )/ ( cos ( f a*pi/270 ) *pow( 1+sqrt(sin(fa*pi/108)*sin((fa*pi/180)/(cos(fa*pi/270) *

cos(b*pi/180))),2)); } }

// **************************************************************// * MIN_D FUNCTION// * Calculate min. embedment depth for stage III of sand excav.// **************************************************************

void min_D(void) { u = y = 0;while (v + Kp/fs*1.5*wtb*bf*y*y*(2*y/3-hh+anc[ j-1]

)

- (sigh+sigs)*(anc[ j-1 ]-hh)*(anc[ j-1 ] -hh)*s/2 - u < 0){ y = y + 0.05;if (gwt >= hh) u = . 0936*bf *Kp/ f s*y*y*( 2*y/3-hh+anc[ j-1 ] )

;

else u = ; }

if ((gwt > hh - y) && (gwt < hh) ) { y = 0;while (v + Kp/fs*1.5*wtb*bf*y*y*(2*y/3-hh+anc[ j-1]) -

93

(sigh+sigs)*(anc[ j-1] -hh)*(anc[ j-l]-hh)*s/2 - 0.0936*bf*Kp/fs*pow((y-hh+gwt) , 2

)*

(

y-hh+anc[ j-1] -

(

y+gwt-hh)/3 ) < 0)

y = y + 0.05; } }

// **************************************************************

// * WT_C_CB FUNCTION// * Calculate average unit weight and cohesion for cut.

// * Also calculate average cohesion for base soils.it **************************************************************

void wt_c_cb( void) {

Ka = 1;

v = 0; y = 0;for (k = 0; hh < soil [k+1] [0 ] ; + +k)

{ if (k >= (nums-1)) break;v = soil[k][l] * (soil[k][0] - soi 1 [k+1 ] [0 ] ) + v;

y = soil[k][2] * (soil[k][0] - soi 1 [k+1 ] [0 ] ) + y; }

v = v + soil[k][l] * (soil[k][0] - hh);y = y + soil[k][2] * (soil[k][0] - hh);if (str_anal == 1) u = 0;else { if ((gwt > hh) && (j < 2)) u = . 0624* ( gwt-hh)

;

else u = 0; }

wt = (v + u) / (telev - hh) ;

ca = y / (telev - hh)

;

int ij, jk; // Calculate the average cohesion over 20 ft.ij = jk = nums-1;while (soil[ jk][0] < hh-20) --jk;while (soil[ij][0] < hh) --ij;if (ij == jk) cb = soil[ij][2];else { y = ; v = hh

;

whi le (ij < jk) {

v = v - soil [i j + 1] [0]

;

y = v * soil[ij][2] + y;v = soil[++i j][0]; }

cb = (y + (20 - hh + soil[ij][0]) * soi 1 [ i j ] [ 2 ] ) / 20; } }

II **************************************************************// * STRIP FUNCTION// * Transform strip load to an equivalent surcharge load and// * add to the surcharge load.// **************************************************************

void strip(void) {

double 01 = atan(qs[2]/(telev-hh) )

;

double 02 = atan( (qs[ 1 ]+qs[ 2 ] )/

(

tel ev-hh) )

;

qe = 2*qs[0]/(pi*Ka)*(O2-Ol) + q; }

94

//////////

*************************************************************** ANCHOR FUNCTION* Perform analysis for wale section modulus, and bonded and* unbonded length for tieback anchor.**************************************************************

void anchor(void) {

clrscr ( )

;

cout << "\n\tEnter the spacingc i n > > d ;

cout << "\n\n\tEnter the angle of thecin >> ang;cout << "\n\n\tSelect soil type:"

of the anchors. --

anchors. --

<< "\n\t Type<< "\n\n\t 1

<< "\n\t 2

<< "\n\t 3

<< "\n\n\t<< "\n\t 5

<< "\n\t 6

<< "\n\t 7

<< "\n\t 8

<< "\n\t 9

<< "\n\t";

Soil Description SPT N Value"Fine to medium sand 12 - 30"Medium to coarse sand 20 - 45"Sandy Gravel > 45"Medium Clay 4-8

Medium Stiff Clay 9 - 11"Stiff Clay 12 - 15"Stiff to Very Stiff Clay 16 - 20"Very Stiff Clay 21 - 30"Very Stiff to Hard Clay > 30"

while ((type = atoi (gets (cc) ) ) <=! ! type >= 10)

{ cout << "\n\t" << cc << " is an incorrect response . \a"

;

cout << "\n\tReenter soil type. -- "; }

for (i = 0; i < numa; ++i) /* Cal . Wale Section Modulus */

{ v = 0;for (j = 0; j < numa; ++j) { if (v < R[i][j]) v = R[i][j]; }

sw[i] = v * d * dP[i] = v * d / (sswitch (type) {

/ (14.4 * s);* cos(ang*pi/180) ) ; // Cal . Anchor Length

pow(10, ((P[i]+68.9)/147) ) ; break;pow(10,((P[i]+7 4.5)/182.4)); break;pow(10,((P[i]+144.2)/298.2)); break;

case 1: L[icase 2: L[icase 3: L[icase 4: L[i] = P[i]/3.14; break;case 5: L[i] = P[i]/4.71; break;case 6: L[i] = P[i]/6.28; break;case 7: L[i] = P[i]/7.85; break;case 8: L[i] = P[i]/9.42; break;case 9: L[i] = P[i]/11.0; break; }

/* Calculate Unbonded Length */ul[i] = ((anc[i]-belev)/sin((45 + ang + f a/2 )*pi/180) ) * sin((45- fa/2)*pi/180); }

clrscr( )

;

cout << "\n\t OUTPUT FROM WALE AND ANCHOR ANALYSIS\n"<< "\n\nSpacing of the anchors is " << d << " feet." <<"\nThe anchors are set at an angle of " << ang << " degrees."

95

<< "\nThe anchors are set in

switch (type) {

"fine to medi"medium to co"sandy gravel"medium clay,"medium stiff"stiff clay.""stiff to ver"very stiff c

"very stiff t

ANCHOR SECTIONUNBONDED")

;

ROW OF WALLENGTH (ft)");

<= numa; ++i) {

%2d %4%4.1f"

" .

coutcoutcoutcoutcoutcoutcoutcoutcout

\n\n

<<<<<<<<<<<<< <

< <

<<

casecasecasecasecasecasecasecasecase

print f

(

ANCHORprintf( "\nLENGTH (ft)

for ( i = 1 ; i

printf ("\n%4.1ful[i-l]); }

if ((type >=1) && (type <= 3))cout << "\n\nNOTE: Tieback capinjected anchors using an" <<"

in excess of 150 psi with a di6 inches and depth of overburd

elsecout << "\n\nNOTE: Tieback capanchors using an effective" <<

excess of 150 psi with a diamefor (i = 0; i < numa; ++i) { ifcout << "\n\nNOTE: FHWA/RD-82/length of 15 feet."; break; }

bp = 3;cout << "\n\n\nPress the enter

'*

.

gets(cc); }

urn sand. " ; break

;

arse sand."; break;."; break;"; break;cl ay

.

" ; break

;

; break;y stiff clay."; break;lay."; break;o hard clay."; break; }

MODULUS ANCHOR

E (in~3) CAPACITY (kips)

.If %4.0fi, sw[i-l], P[i-1], L[i-1],

acity is based on pressure\n effective grout pressureameter" <<"\n between 4 toen greater than 13 feet.";

acity is based on post-grouted"\n grout pressure inter of six inches.";(ul[i] < 15) {

047 recommends a minimum unbonded}

key to return to the main menu.

// ******************************************************// * SAVE FUNCTION// * Save the results from the various analysis functions.// **************************************************************

void save(void) {

FILE *xp;cl rscr ( )

;

cout << "\n\tEnter filename to save the data. -- ";

gets( f i 1 ename)

;

while ((xp=fopen(filename,"r")) != NULL) {

cout << "\n\tThe file already exits, do you want to overwrite it?(Y/N) -- \a";

96

gets( cc)

;

c = toupper(cc[0] )

;

switch (c) {

case '

Y' : break;

case 'N' : cl rscr( )

;

cout << "\n\tReenter the filename. -- ";

gets( f i 1 ename) ; break;default :

cout << "\n\t" << cc << " is an incorrect response, try again-- \a";

gets(cc)

;

c = toupper ( cc[0 ] ) ; }

if (c == 'Y' ) { c = 'x' ; break; } }

xp = fopen( filename , "w+");fprintf (xp, "\n\n");fprintf (xp, "\t******************************************************fprintf (xp, "\t* *

fprintf (xp, "\t* Design of Soldier Pile and Lagging *

fprintf (xp, "\t* In Accordance with NAVFAC DM-7 *

fprintf (xp, "\t* *

\n")

\n")

\n")

\n")

\n")fprintf (xp, "\t****************************************************** \n"

)

fprintf (xp, "\n\n\tl. WALL PROPERTIE S\n");fprintf (xp, "\n\tl. Engineer: %s", engineer);fprintf (xp, "\n\t2. Project: %s", project);fprintf (xp, "\n\t3. Date: %s", date);fprintf (xp, "\n\t4. The elevation of the top of the excavationis %4.2f feet.", telev);fprintf (xp, "\n\t5. The elevation of the bottom of theexcavation is %4.2f feet.", belev);fprintf (xp, "\n\t6. The number of anchors is %d.", numa);if ( numa ) {

fprintf (xp, "\n\t The anchors are located as f ol lows: \n")

;

fprintf (xp, "\t\tAnchor\tElevation (feet)\n M);

J = 0;for (i = 0; i < numa; + + i) {fprintf(xp, "\t\t %2d\t%5.2f\n", + +j, anc[i]); } }

fprintf (xp, "\n\t7 . The spacing of the soldier piles is %3.2ffeet.", s);

fprintf (xp, "\n\n\n\tll . SOIL PROPERTIE S");fprintf (xp, "\n\n\t8. The elevation of the water table is %6.2ffeet.", gwt);

fprintf (xp, "\n\t9. The soil properties are as follow:\n");fprintf (xp, "\n\t Soil Type Elev Unit Wt

97

Friction Angle")

;

fprintf (xp, "\n\tor Cohesion") ; j = ;

for (i = 0; i < nums; ++i) {

fprintf (xp, "\n\t ");

if (soil_type == 1) fprintf (xp, "sand");else fprintf (xp, "clay");fprintf (xp, " %7.2f %1.4f %5.2f",soil[j][0], soil[j][l], soil[j][2]);j++; }

fprintf (xp, "\n\n\tl0. The slope of the ground behind the wallis %2 . 2f degrees .

" , b)

;

fprintf (xp, "\n\tll. The surcharge load is %3.3f ksf.", q);fprintf (xp, "\n\tl2. The strip load is %7.2f ksf, %4.2f feetwide,", qs[0], qs[l]);fprintf (xp, "\n\t and located %5.1f feet from the wall.",qs[2]);fprintf (xp, "\n\n\n\tIII. WALL ANALYSIS RESULT S");fprintf (xp, "\n\n\tl3. Estimated width of the soldier pile is%3.2f feet.", bf);fprintf (xp, "\n\tl4. Factor of safety for passive resistance is%3.1f.", fs);fprintf (xp, "\n\tl5. The wall was excavated %3.1f feet belowthe proposed anchor location.", w);

fprintf (xp, "\n\n\tl6. STAGE ZEROEMBEDMENT REACTION( S) " )

;

fprintf (xp, "\n\t SHEARDEPTH" )

*

fprintf (xp, "\n\t (ft) (k-ft) (iiT3) (ft)(kips)");

fprintf (xp, "\n\t");

fprintf (xp, "\n\t 1 %6.1f %6.2f---", z[0], M[0], S[0], D[0]);

j = 0;for (i = 2; i <= numa + 1; ++i) {

fprintf (xp, "\n\t %d %6.1f %6.2fRl = %6.2f", i, z[i-l], M[i-1], S[i-1], D[i-1], R[0][j]);

for (k = 2; k <= numa; ++k) {

if (R[k-l][j]) {

fprintf (xp, "\n\t\t\t\t\t\t\t R%d = ", k);fprintf (xp, "%6.2f", R[k-l][j]); } }

++j; }

fprintf(xp, "\n\n NOTE: Stage 1 moment based on Kiewit criteriais %6.1f kip-ft.", Mk[0]);

if (numa > 0) {

fprintf(xp, "\n Stage 2 moment based on Kiewit criteriais %6.1f kip-ft", Mk[l]);

MAXIMUM SECTION

MOMENT MODULUS

(k-ft) (in~3)

%6.2f %6.1f

%6.2f %6.1f

98

fprintf(xp, "\n and reaction force is %6.1f kips ."

, P.k ) ; }

i f ( numa > 1 )

fprintf (xp, "\n\n NOTE: Minimum depth of embedment based onmaximum moment is %3.1f feet.", Dmin);

if ((D[numa] < 6) !! (Dmin < 6)) {

fprintf ( xp , "\n\n NOTE: NYCTA recommends minimum penetrationdepth of six feet."); }

if ((soil_type == 2) && (str_anal == 1))fprintf (xp, "\n\n NOTE: A total stress analysis approach wasused.");

if ((soil_type == 2) && (str_anal == 2))fprintf (xp, "\n\n NOTE: An effective stress analysis approachwas used. " )

;

if (bp > 2) {

fprintf (xp, "\n\n\n\tIV. ANCHOR AND WALE RESU L T S")

;

fprintf (xp, "\n\n\tl7. Spacing of the anchors is %3.1f feet.",d);fprintf (xp, "\n\tl8. The anchors are set at an angle of %3.1fdegrees .

" , ang)

;

fprintf (xp, "\n\tl9. The anchors are set in ");switch (type) {

"fine to medium sand."); break;"medium to coarse sand."); break;"sandy gravel."); break;"medium clay."); break;"medium stiff clay."); break;"stiff clay."); break;"stiff to very stiff clay."); break;"very stiff clay."); break;"very stiff to hard clay."); break; }

case 1 fprintf 1[xp,case 2 fprintf l

!xp,

case 3 fprintf 1Ixp,

case 4 fprintf 1[xp,case 5 fprintf 1 . xp,case 6 fprintf <

[ xp,case 7 fprintf '

kxp,

case 8 fprintf I[xp,

case 9 fprintf I»xp,

fprintf (xp, "\n\t20.\n")

;

fprintf (xp, "\n ANCHOR SECTION MODULUSANCHOR UNBONDED");fprintf (xp, "\n ROW OF WALE (in~3)LENGTH (ft) LENGTH (ft)");fprintf (xp, "\n

ANCHOR

CAPACITY (kips)

);

%4.1f %4.0fi, sw[i-l], P[i-1], L[i-1],

for (i = 1; i <= numa; ++i) {

fprintf (xp, "\n %2d%4.1f %4.1f",

ul[i-l]); }

if ((type >=1) && (type <= 3)) {

fprintf (xp, "\n\n NOTE: Tieback capacity is based on pressureinjected anchors using an");fprintf ( xp , "\n effective grout pressure in excess of150 psi with a diameter");

fprintf ( xp , "\n between 4 to 6 inches and depth ofoverburden greater than 13 feet."); }

99

else {

fprintf (xp, "\n\n NOTE: Tieback capacity is based on post-grouted anchors using an effective");

fprintf (xp, "\n grout pressure in excess of 150 psi

with a diameter of six inches."); }

for (i = 0; i < numa; ++i) { if (ul[i] < 15) {

fprintf (xp, "\n\n NOTE: FHWA/RD-82/047 recommends a minimumunbonded length of 15 feet."); break; } } }

fprintf (xp, "\n\n\t\t\tE ND OF ANALYSI SM);

fprintf (xp, "\n\n");f close( xp)

;

cout << "\n\tData saved, press the enter key to return to themain menu. "; gets(cc);// *******************************************************

// * END OF PROGRAMII **************************************************************

}

100

APPENDIX C

CALCULATIONS AND EQUATIONS

101

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COS (0-9)

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112

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)

Figure C.lAverage Load Capacity of Anchors in Fine to

Medium Sands

250 -i

+

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fedim Orrcse

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IXI

Length of Anchor (ft)

Figure C.2Average Load Capacity of Anchors in Medium

To Coarse Sands

115

Length of Anchor (( t

)

Figure C.3Average Load Capacity of Anchors in Sandy Gravel

116

APPENDIX D

EXAMPLE PROBLEMS

117

************************************************* *



* *

************************************************

I. WALL PROPERTIES1. Engineer: D' Amanda2. Project: Sand Example #13. Date: 21 September 19914. The elevation of the top of the excavation is




1 245.002 235.003 225.00


II. SOIL PROPERTIES8. The elevation of the water table is 0.00 feet.9. The soil properties are as follow:


sand 250.00 0.1100 30.00


.

11. The surcharge load is 0.500 ksf.12. The strip load is 5.00 ksf, 20.00 feet long,

and located 50.0 feet from the wall.


anchor location.

118

16. STAGE ZERO MAXIMUM SECTION EMBEDMENT REACTION(S)SHEAR MOMENT MODULUS DEPTH(ft) (k-ft) (iiT3) (ft) (kips)

1 11.0 57 53 23. 97 9.52 22.9 59 63 24.84 5.8 Rl = 31.243 20.5 71 43 29.76 5. 4 Rl =

R2 =

53.1343.68

4 30.0 73 45 30.60 5.7 Rl =

R2 =

R3 =

66.1051.4158.76

NOTE: Stage 1 moment based on Kiewit criteria is 43.5kip-ft .

Stage 2 moment based on Kiewit criteria is 44.2kip-ft and reaction force is 27.2 kips.



IV ANCHOR AND WALE RESULTS17181920

Spacing of the anchors is 8.0 feet.The anchors are set at an angle of 5.0 degrees.The anchors are set in medium to coarse sand.

ANCHOR SECTION MODULUS ANCHOR ANCHOR UNBONDEDROW OF WALE CAPACITY LENGTH LENGTH

(in~3) (kips) (ft) (ft)

73.457.165.3

133103118

13.79.4

11.4

16.611.05.5

NOTE: Tieback capacity is based on pressure injectedanchors using an effective grout pressure inexcess of 150 psi with a diameter between 4 to 6

inches and depth of overburden greater than 13feet.


END O F ANALYSIS

119

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126

************************************************* *



* *

************************************************

WALL PROPERTIES1. Engineer: D' Amanda2. Project: Sand Example #23. Date: 21 September 19914. The elevation of the top of the excavation is


-10.00 feet.6. The number of anchors is 2.


1 5.002 -5.00


II SOIL PROPERTIES8. The elevation of the water table is 0.00 feet9. The soil properties are as follow:

Soil Type

sandsandsand

Elev

10.003.00

-4.00

Unit Wt

0.11000.11500.1180

Friction Angleor Cohesion

30.0035.0038.00


.



Ill WALL ANALYSIS RESULTS13. Estimated width of the soldier pile is 1.00 feet.14. Factor of safety for passive resistance is 1.0.15. The wall was excavated 1.0 feet below the proposed

anchor location.

127


1 10.9 32.85 13.69 9.72 23.6 43.25 18.02 6.6 Rl = 23.563 17.5 12.32 5.14 3.8 Rl =

R2 =

44.3724.65

NOTE: Stage 1 moment based on Kiewit criteria is 25.2kip-ft.Stage 2 moment based on Kiewit criteria is 44.3kip-ft and reaction force is 18.9 kips.


NOTE: NYCTA recommends minimum penetration depth ofsix feet

.

IV ANCHOR AND WALE RESULTS17181920

Spacing of the anchors is 9.0 feet.The anchors are set at an angle of 10.0 degrees.The anchors are set in fine to medium sand.


(inA3) (kips) (ft) (ft)

27.715.4

4525

6.04.4

7.42.5

NOTE: Tieback capacity is based on pressure injectedanchors using an effective grout pressure inexcess of 150 psi with a diameter between 4 to 6

inches and depth of overburden greater than 13feet.


END O F ANALYSIS

128

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131

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135

************************************************* *


* In Accordance with NAVFAC DM-7 ** *

************************************************

WALL PROPERTIES1. Engineer: D' Amanda2. Project: Clay Example #13. Date: 21 September 19914. The elevation of the top of the excavation is




1 90.002 80.003 70.00


II SOIL PROPERTIES8. The elevation of the water table is 0.00 feet.9. The soil properties are as follow:


clay 100.00 0.1100 0.50clay 85.00 0.1200 1.75

10. The slope of the ground behind the wall isdegrees

.



Ill WALL ANALYSIS RESULTS13. Estimated width of the soldier pile is 1.00 feet.14. Factor of safety for passive resistance is 1.0.15. The wall was excavated 1.0 feet below the proposed

anchor location.

136


1 13.6 119.25 49.692 24.3 91.14 37.983 25.1 150.38 62.66

4 34.7 123.01 51.25

7.52.12.2

2.1

Rl = 44.13Rl = 194.47R2 = 80.75Rl = 211.11R2 = 103.15R3 = 128.81



NOTE: NYCTA recommends minimum penetration depth ofsix feet

.

NOTE

IV.

17.18.19.20.

A total stress analysis approach was used.

ANCHOR AND WALE RESULTSSpacing of the anchors is 5.0 feet.The anchors are set at an angle of 7.5 degrees.The anchors are set in stiff to very stiff clay


(irT3) (kips) (ft) (ft)

1 73.32 35.83 44.7

213 27.1 26.7104 13.3 17.8130 16.5 8.9

NOTE: Tieback capacity is based on post-groutedanchors using an effective grout pressure inexcess of 150 psi with a diameter of sixinches

.


END O F ANALYSI S

137

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************************************************* *



* *

************************************************

I. WALL PROPERTIES1. Engineer: D' Amanda2. Project: Clay Example #23. Date: 21 September 19914. The elevation of the top of the excavation is




1 1630.002 1620.00


II. SOIL PROPERTIES8. The elevation of the water table is 1637.00 feet.9. The soil properties are as follow:


clay 1637.0 0.0626 0.75

10. The slope of the ground behind the wall isdegrees

.




anchor location.

148

16. STAGE ZERO MAXIMUM SECTION EMBEDMENT REACTION(S)SHEAR MOMENT MODULUS DEPTH(ft) (k-ft) (irT3) (ft) (kips)

1 0.0 0.00 0.00 0.02 23.5 5.39 2.24 5.1 Rl = 4.263 20.0 41.81 17.42 4.4 Rl =

R2 =

65.6065.84




NOTE: A effective stress analysis approach was used.

END OF ANALYSIS

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APPENDIX E

REFERENCES

154

American Institute of Steel Construction, Manual of

Steel Construction, Eighth Edition, Illinois, 1980.

Boghrat, Alireza, "Use of STABL Program in Tie-BackWall Design", Journal of Geotechnical Engineering ,

Volume 115, No. 4, pp. 546-552, New York, April 1989

Bowles, Joseph E., Foundation Analysis and Design ,

Fourth Edition, McGraw-Hill Book Company, New York,1988.

Carpenter, J. R., and S. Kopperman, U.S. Department ofTransportation, Federal Highway Administration,PCSTABL4 User Manual , Report Number FHWA-TS-85-229 , U.SGovernment Printing Office, Washington, D.C., 1985.

Cernica, John N., Geotechnical Engineering , Holt,Ricnehart and Wiston, New York, 1982.

Chapman K. R. , E. J. Cording, H. Schnabel , Jr.,"Performance of Braced Excavations in Granular andCohesive Soils", Proceedings of the SpecialtyConference on Performance of Earth and Earth-SupportedStructures , American Society of Civil Engineers, VolumeIII, pp. 271-293, New York, 1972.

Clough, G. Wayne, "Performance of Tie-Back SupportSystems", Proceedings of the Specialty Conference onPerformance of Earth and Earth-Supported Structures ,

American Society of Civil Engineers, Volume III, pp.259-264, New York, 1972.

Das, Braja M. , Principles of Foundation Engineering ,

Second Edition, PWS-Kent Publishing Company,Massachusetts, 1990.

155

Goldberg, D. T . , W. E. Jaworski , and M. D. Gordon, U.S.Department of Transportation, Federal HighwayAdministration, Lateral Support Systems andUnderpinning , Volume I Design and Construction, ReportNo. FHWA/RD-75/128, U.S. Government Printing Office,Washington, D.C., 1976.

Jarquio, Ramon, "Total Lateral Surcharge Pressure Dueto Strip Load", J ournal of the Geotechnical Engineeri ngDivision , Proceedings of the American Society of CivilEngineers, Vol. 107, No. GT10 , pp. 1424-1428, New York,October 1981.

Keorner, Robert M. , Construction and GeotechnicalMethods in Foundation Engineering , McGraw-Hill BookCompany, New York, 1984.

Lambe, T. William, and Edmund K. Turner, "BracedExcavations", Lateral Stresses in the Ground and Designof Earth-Retaining Structures , State-of -the-Art Paperspresented at 1970 Specialty Conference, Soil Mechanicsand Foundations Division, American Society of CivilEngineers, New York, 1970.

Lambe, T. William, and Robert V. Whitman, Soi

1

Mechanics , John Wiley & Sons, New York, 1969.

Liao, Sam S.C., and Thorn L. Neff, "Estimating LateralEarth Pressures for Design of Excavation Support",Design and Performance of Earth Retaining Structures ,

Proceedings of a Conference, Geotechnical EngineeringDivision of American Society of Civil Engineers, NewYork, June 18-21, 1990

Merritt, Frederick S., Standard Handbook for Engineers ,

McGraw-Hill Book Company, New York, 1976.

New York City Transit Authority (NYCTA), EngineeringDepartment, Civil Engineering and ArchitecturalDivision, Field Design Standards, 1974.

156

Ostermayer, H., "Construction. Carrying Behavior andCreep Characteristics of Ground Anchors", Proceeding ofDiaphragm Wall and Anchorages Conference ,

Institute of Civil Engineers, pp. 141-151, London,England, 1975.

Peck, R. B., "Deep Excavations and Tunneling in SoftGround", Proceedings, Seventh I.C.S.M.F.E, State of theArt Volume , pp. 225-290, Mexico, 1969.

Terzaghi, K. and P. B. Peck, Soil Mechanics inEngineering Practice , Second Edition, Wiley, NewYork, 1967.

Turbo C++ User's Guide , Second Edition, BorlandInternational Inc., California, 1991

U. S. Department of the Navy, Naval FacilitiesEngineering Command, Foundations and Earth Structures ,

Design Manual 7.2 (NAVFAC DM-7.2), Washington, D.C.,1982.

Ulrich, Edward J., Jr., "Tieback Supported Cuts inOverconsol idated Soils", Journal of GeotechnicalEngineering , Volume 115, No. 4, pp. 521-545, New York,April 1989.

U. S. Department of Transportation, Federal HighwayAdministration, Tiebacks , Report No. FHWA/RD-82/047

,

U. S. Government Printing Office, Washington, D.C.,1982.

157

)o

ThesisD14727c.l

D ' AmandaComputer aided design

of soldier pile and lag-ging retaining wallswith tieback anchors.

Thesis

D14727c.l

D ' AmandaComputer aided design

of soldier pile and lag-

ging retaining walls

with tieback anchors.

*1?KA.

Documents

Computer aided design of soldier pile and lagging ... · Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 1991 Computer aided design of soldier pile